The answer is 1:

I have misunderstood the paragraph, and the author does indeed believe that boringest is grammatical.

The statements to the contrary (2 and 3) rely on inferences from a reading of the rest of the paragraph where the author believes strictly in the rules he lays out. However, in examining the paragraph there is plenty of room for the overall paragraph and the final sentence, as stated, to be consistent with one another. The author does not believe that strict rules are the only basis of grammaticality; the author does not believe frequency is an assessment of grammaticality. I will offer a paragraph-level reading and then a paper-level reading to show how the author's statement is consistent with his immediate meaning and his general approach.

Paragraph-level reading

The first four sentences introduce the use of a corpus in linguistic research. Sentence 2 states the ease of using digital corpora for studying vocabulary frequency and grammar. Sentence 3 sets up an assumption that some users of corpora make - there is a relationship between the frequency of a construction and linguistic status. Sentence 4 elaborates on that logic: common means "fully grammatical," and rarity marks it as dubious:

A corpus is “… a body of texts put together in a principled way, often for the purposes of linguistic research.” (Johansson 1991: 3). Computer technology means that modern corpora are large and easy to manipulate, thus lending themselves well to frequency studies of vocabulary and, to a lesser extent (Granger 2002: 21), grammar. The assumption is that there is a relationship between how frequent a construction is attested and its status in the language. Common forms and structures will be fully grammatical, rarer items dubious.

Sentence 3 and 4 are both working on an assumption that frequency should be used to judge grammaticality. However, nothing identifies this as the author's own assumption; instead, the author uses language that distances himself from that assumption: "the assumption is" following two sentences sourced respectively to two other authors, Johansson and Granger.

What follows is an example of this assumption at work. The first sentence states a grammatical tendency relating to the formation of comparatives and superlatives through periphrasis (e.g. more alarming) and not morphology (e.g. (x)alarminger). The second sentence compares this rule to corpus frequency. The third sentence adds a complication to the assumption - there is one formation in the BNC that deviates from the tendency:

For example, -ing adjectives such as alarming, gratifying, mocking form comparatives and superlatives through periphrasis not morphology (Biber, Johansson, Leech, Conrad, and Finegan, 1999: 523), hence more/most alarming instead of *alarminger/est. Frequency data confirm this rule. The only exception found in the British National Corpus is this one occurrence of boringest: ‘…it’s always the boringest people, I’ve never seen any of them smile, laugh, talk…’.

What is to be done here? The author discusses the situation of this possible counterexample. Because the word appears but is infrequent, he has to admit a lack of evidence for this to be a "competing form." In the next two sentences, the author then states a contextual reason for the usage to come up - "boringest" as an unusual form may show the distinct personality of the person using it. "Boringest" is "marked" or emphatic:

There is not enough evidence to suggest that boringest is a competing form to the standard most boring. In the concordance line quoted, the speaker may want to highlight how dull these people are by contrasting his/her own interesting personality. The adoption of the marked form boringest shows individuality and an unconventional streak, distancing the speaker from the people being denigrated.

Now this is where I think a lot of readings make an incorrect assumption. Even if they were clear that the author was discussing assumptions made by corpus researchers, they might assume that the example affirming that boringest is an unusual form meant that it was an ungrammatical form. However, in the last few sentences the author has focused instead on marked langauge, on individuality, on an unconventional streak. That leads the author to distinguish these features - stylistics - from grammar, to say that the corpus shows evidence of stylistics.

But this is the domain of stylistics, not grammar.

Indeed, for this author, what researchers are studying in frequency analysis is stylistics. The question of grammaticality need not correlate with that. Thus he makes this bold claim:

There is no question that boringest belongs to the grammar of standard English.

Now, that is evidently a controversial statement, based on the responses to this question. So the statement may be incorrect, and it may benefit from further elaboration. However, within the context of this author's argument in this paragraph, the denotative meaning fits. Corpus frequency spoke to stylistics, not grammar, and so despite the low frequency boringest is (for the author) grammatical.

Paper-level reading

Now, regarding the paper as a whole, this interpretation of the sentence fits, according to a few points of evidence:

The abstract sets up the paper as an examination of individual readings of decontextualized sentences as a judgment of grammaticality -

A standard method of determining whether a construction is well-formed is a grammaticality judgment test, where subjects make an intuitive pronouncement on the accuracy of form and structure in individual decontextualized sentences ...

as compared with several sometimes-conflicting sources of evidence:

evidence on the frequency of usage, from corpora, and internal linguistic criteria

So the abstract leads one to expect that different forms of evaluating grammar will be compared, without necessarily holding one (like corpus frequency searching) as more important.

Then the introduction develops further an idea that, when the author is examining the assessment of error by others, he does so in a context that regards some items considered "errors" as productive language usage:

For instance, one critic’s error is often another critic’s creativity: according to Cook (2000), our natural penchant for playing with language takes us into the territory where accuracy loses its boundaries. This process is actually associated with highly-developed language competence because it demands great sensitivity to language norms and awareness of occasions when they can be eased or broken.

That fits in with the author's description of the individual who used boringest - they are individual and creative, and may involve "highly-developed language competence." The author refers to an outside source to make this claim, but does not describe it as an outside assumption - he says "this process is actually associated," indicating a belief in the actuality of the statement.

By the end of the introduction, the author clarifies that he draws a distinction between obvious errors (like "four furnitures") and then suggests that there may be grammatical usage that doesn't correspond to standard rules (like his example of "boringest" suggests):

Error is a reality of language use and dealing with grammar that does not conform to a rule-based description of the standard language presents theoretical and practical challenges.

Note that this is an adequate response to sumelic's concern that the author believes in the periphrastic rule universally, that boringest cannot be (a) an exception and (b) grammatical. Yet, if the author acknowledges the existence of grammar that doesn't conform to rules, then it makes sense that both examples described by the rule and its exception (boringest) could be grammatical.

The remainder of the paper uses responses from English language teachers to study three kinds of appeals used in arguing for grammaticality. The author takes neither of their sides. The conclusion assess the difficulty of using either corpus-based methods or a series of individual judgments to assess grammaticality:

Indeed, grammaticality judgment tests share one of the more disconcerting side-effects of the plethora of corpus studies, namely a lack of confidence in grammatical description.

In other words, corpus tests aren't very reliable at assessing grammaticality. That's the very assumption that would allow the author to state that boringest is grammatical despite the corpus evidence.

Summary

Given the paragraph-level evidence and the paper-level evidence, the statement

There is no question that boringest belongs to the grammar of standard English

makes sense as literally stated. It is consistent with his paragraph-level point that corpus frequency analysis focuses on stylistics and not grammar, and it fits an overall paper that compares two kinds of frequency analysis (corpus usage, individual assessments) in order to say that they have a probability of being correct but are not always so. That said, many of us readers would prefer the author elaborate on why the author thinks its grammaticality should go unquestioned.