In the sentence They gave [object], the object is singular when the group collectively gives a single thing. In your example, They gave their word, the group collectively makes the same promise. In contrast, They gave their lives says that each member of the group devoted or sacrificed their individual lives – even if they shared a common cause.
This is true for all transitive verbs. For example, if a group of comrades make a conference call (or even a series of calls) to a single person, They called their friend. However, if they each make individual calls to separate people, They called their friends.
EDIT: Also note that we don't always pluralize abstract nouns in English. The more abstract the noun, the more likely we are to use it collectively. That's why plural consciousnesses sounds awkward even when talking about multiple minds: We usually think of minds concretely, consciousness in the abstract.
In many cases, you can use a noun either way. Choosing to pluralize or not helps to emphasize whether you mean it concretely or in the abstract. For example, All presidents swear an oath to uphold the Constitution of the United States. This emphasizes that all presidents make an oath of the same nature, even though they all do it individually. They all give their word.
In contrast, we usually write that they devote their lives to upholding the Constitution to emphasize the individual nature of their contributions. You could write that as singular life instead to emphasize the common, abstract nature of their devotion, but we usually don't.
"Here's" seems to be used before plurals in colloquial contexts
"Here's the details" doesn't seem strange to me in a colloquial context. I agree with the comparison to "there's." You can see from the comments beneath your question that there are a fair amount of examples in English-language corpora (I can't verify this information at the moment, but it shouldn't be too hard to check if you doubt this).
The prescribed "correct" form is "Here are [plural noun phrase]"
You already know this. I don't think there's much more to say about that subject. Of course, different people have different levels of deviation from the prescribed standard and tolerance for such deviations by other people.
It is grammatical, if we use a linguist's definition of "grammatical"
"Ungrammatical" is not really well-defined in the sense it is used in that quotation. If the author just meant that "Here are the details" is preferable when writing for publication, I agree.
Arguably, though, "here's [plural noun]" is more consistent with the underlying grammar that native English speakers acquire than "Here are [plural noun]". Nicholas Sobin argued in "Agreement, Default Rules, and Grammatical Viruses" that plural agreement in expletive constructions such as "There's" is actually a "linguistically deviant" phenomenon that occurs as a special prestige form not generated by the grammar of English (the supposed mechanism for this is described by his "grammatical virus" theory).
The "grammatical virus" analysis of plural agreement has been contested by some other linguists (for a more recent paper on the subject that discusses some of the subsequent literature, see Fournier), but the reason I bring this up is to point out that it's not as simple as it might seem to figure out how grammar works.
And in fact, it seems like Schütze, one of the critics of the "grammatical virus" explanation for plural agreement in expletives, agrees with Sobin that singular agreement with plural nouns is grammatical (Schütze just thinks that plural agreement is also grammatical).
All of the previously-mentioned papers seem to focus on the "There's/There is/There are" construction. However, "here" is also an expletive, so it seems likely that the same or similar grammatical principles apply to the "Here's/Here is/Here are" construction. Edwin Ashworth found an example with "Here's" in Schütze that is taken from a 1984 paper by Randall B. Sparks titled "Here's a Few More Facts". Sparks notes that 's may also occur before a plural noun in questions beginning with where, when, how and what (such as "Where's my pants") and proposes that it occurs in declarative sentences "that are possible answers to these types of questions" (Sparks 180).
Bibliography
Fournier, David H. "There's some Problems: Complex Subject Agreement in English and Virus Theory."
Schütze, Carson T. "English Expletive Constructions Are Not Infected."
Sobin, Nicholas. "Agreement, Default Rules, and Grammatical Viruses." Linguistic Inquiry Vol. 28, No. 2 (Spring, 1997), 318-343.
Sparks, Randall B. "Here's a Few More Facts." Linguistic Inquiry Vol. 15, No. 1 (Winter, 1984), 179-183.
Also, after writing this answer I found something written by Sobin that is accessible (at least for me) from Google Books, "Prestige English Is Not a Natural Language"
Best Answer
They pull their ears would be grammatically correct. However, it does not convey whether the theys pull one or two ears. (The possibility that they pull the ear or ears of someone else in the group is a third possibility, but so unlikely as to not be a real issue).
There are a number of ways to convey that only one ear per person is being pulled is