Apparently conoscere, as used in the Passato Remoto, is always understood to mean "to meet".
To say "knew" we would normally use the Imperfetto, even if this is in the remote past. Even if the subject no longer knows the person, e.g. in the extreme case that both of them are long dead. I primi umani conoscevano i loro genitori.
You'd say "conoscevamo" if you were speaking in the Imperfect Past, not the Passato Remoto. And the idea that one cannot use "conoscemmo" to mean "knew" in the Passato Remoto because it implies that we no longer know the writer only makes sense if you are speaking to a moron. How do we "un-know" someone??? I'm only a neophyte, but I suspect that the uses of "conoscemmo" to mean both "met" and "knew" in the remote past are interchangeable. And if they are not, they certainly should be. Perhaps an Italian native speaker can help???
But your suspicion is incorrect. "Conoscere" is one of the verbs that takes on different English meanings with different Italian conjugations (like, for example, "dovere"). So yes, in the passato remoto, "conoscere" means "to meet," because it's referring to a one-time event of a fixed duration.
If you want to talk about knowing someone, that's an ongoing state (as you said, we can't "un-know" someone), so it requires the imperfect.
Thank you for this. As infuriating as the facts are, I have to defer to your fluency and understanding. So my question then becomes, is there no Passato Remoto form of knowing someone from long ago, e.g., "I knew a man when I was a child who taught me to whistle"? It just seems to me that to use the Imperfetto betrays the very purpose of the form.
Something like "when I was a child" will always take the imperfect, because it's an amorphous amount of time (or if that doesn't make sense, because that's just how Italian grammar has developed). The reason that "conoscere" doesn't really work with a fixed duration is that to get out of the imperfect, you'd have to say something like "I knew him for exactly three years," which doesn't make a whole lot of sense.
The same thing happens with "sapere" in the past. If you said "Ho saputo [di qualcosa]," it usually translates to "I found [something] out." The quality of knowing can't really be fixed in duration.
Not to belabor the point, and I can accept it as a rule, but this explanation doesn't really make sense to me. I would indeed say something like "years ago, when we lived in New York, we knew a writer," in the sense that we haven't been in touch for years, so we don't technically know them anymore, we don't have contact, etc. You can, indeed, stop knowing someone especially if a lot of time has passed. People are not static—they change. So apart from accepting it as a rule in Italian, it doesn't really make sense to me that it can't mean "to know" in the passato remoto. To me, the further back you go in time, the more sense it makes. In English we say this kind of thing all the time.
Your example still uses the imperfect, because you're talking about a vague, nebulous time period. Similarly, "When I was young, I read books" becomes "Quando ero giovane, leggevo libri," even though I clearly finished those books at some point. The issue isn't that the event ended; it's that the duration is mushy.
And again, this is just a rule of how "conoscere" works. When translated in the simple past, it only means "to meet," not "to know." You can come up with various reasons that you don't like that rule, but that's the rule.
It depends on how you're using "met". If you mean "met" as in had a meeting with, then "incontrammo" would be acceptable. But if we're talking about meeting someone in the sense of a first introduction to a person, then "conoscemmo" is the correct verb to go with.
But if they didn't accept "incontrammo", I'd report it. Without context, either meaning of "met" is acceptable here.
Because (as explained in comments above), that's the meaning "conoscere" takes in the past and the present/past perfect tense. Here's some more examples of how that meaning changes with both "sapere" and "conoscere": https://www.thoughtco.com/italian-verbs-sapere-conoscere-2011690