"He doesn't know who they are" was accepted for me just now (1/4/15) - then again, maybe it was an April Fool joke! :P
It said the right answer was "He doesn't know who they're", but contracted forms of "be" can't end a sentence.
So "he does not know who I am" and "he does not know who they are" are both correct. I may never get this stuff. How is one to know which of those statements is intended. AGHHHH!
Duo accepts either. If you were having a real live conversation with real live Italians, then you would have context to explain which of the alternatives applies.
A rule that seems to apply in other languages which have a similar Sapere vs Conoscere dichotomy is that Sapere-type verbs are usually followed by a verb in a subordinate clause, and Conoscere-type verbs usually take a noun. So, in this case you would have "Lui non mi conosce".
I grant you that the division seems to be fuzzier in Italian, though!