This lack of respect for the language of origin not a phenomenon unique to English. When a word is borrowed into one language from another, unexpected things can happen.
I would argue that, for many examples you've given in your question, the actual perception of a singular-plural relationship is messy in practice, and the application of the plural is inconsistent.
Data: Using data as a collective noun with singular agreement is more common than using it with plural agreement. More in another thread from this site.
Alumni: I have heard as many people also use alumni for the singular, or even alum, as I have heard use alumnus for the singular. I imagine my experience with this word is typical (at least in the US), though certainly not universal. In any case, it is messy.
Media: The words media and medium don't even seem to correspond in any meaningful way in actual English usage. The word media has forked off and become a different word entirely. The word media is clearly used as a collective singular noun, as shown in newer constructions like multimedia (not multimedium even though we don't say multistages, multicores, multicycles, multistories, etc.). You will find few people who will ever say "Mass Medium". We talk about someone having "media savvy" even though we wouldn't say "computers savvy" (even though they can work with more than one computer). This is because, in English, these sorts of constructions always use the singular noun, whether it is collective or not. The way that media is used is evidence of how the word is actually parsed, perceived, and used by English speakers.
Another example of how foreign language morphology often doesn't mesh well: people try to pluralize octopus and virus as octopi and viri/virii, respectively. Virus was a mass noun in Latin, where we got the word. The word octopus comes from Greek and would take the plural form octopodes in Greek.
My main point is this: there is only a weak, inconsistent application of this -us to -a or -us to -i to begin with. So forums (like statuses and others) is a word even though we also sometimes have this other rule. Our language seems to continually push us towards either dropping the foreign pluralization in some way or another, or reanalyzing the plural as another distinct word. So I see this confusion as the language trying to mash these words around to make them fit our language naturally.
If we hadn't become so darn literate and knowledgeable in the past few centuries, I imagine these plurals would have regularized by now :)
Best Answer
First, let's expand the contraction to clearly show the subject and the verb:
That is two words.
"That"--demonstrative pronoun (singular) [https://en.wikipedia.org/wiki/That ]
"is"--a linking verb (singular; NOT an action verb).
When a linking verb is used
"A linking verb ("is," "are," "was," "were," "seem" and others) agrees with its subject, not its complement."
[ https://writing.wisc.edu/handbook/grammarpunct/subjectverb/ ]
"words"--subject complement (quantified by "two"--numeral determiner)
"A subject complement follows a linking verb; it is normally an adjective or a noun that renames or defines in some way the subject."
[http://grammar.ccc.commnet.edu/grammar/objects.htm ]
Based on that, I don't think it would've mattered if there were 1000 words, as long as "that" referred to something singular, such as an essay...or, another example, a Stephen King novel: I read Duma Key. That's 609 pages!
The last page is two sentences:
Know when you're finished, and when you are, put your pencil or your paintbrush down. All the rest is only life.
(Which reminds me, something singular, as I put it, may be a mass noun, not necessarily a countable noun, if I'm not mistaken...but I'm finished now.)