I want to state at the onset, I have no personal opinion on this matter, I'm simply elucidating the logic of it:
In general, the genetic fallacy is the illegitimate rejection of an argument strictly on the basis of its origin. It is considered a fallacy because a valid argument cannot be made invalid by changing its origin. Like all fallacies, it gains its force because of its close but superficial similarities to more legitimate lines of argument.
In this particular case, your interlocutor is advancing an implicit argument of [his] own. That argument (we can infer) is that because the AATA is (putatively) committed to a certain core position on an certain issue of history, they are likely to endorse other positions that align with that first one, regardless of whether or not those positions are true.
It's definitely not a strong argument --no open and shut case --but it's not necessarily fallacious. In particular, it's not the genetic fallacy due to the fact that there is actually a relationship between the premise "A believes X" and the conclusion "A claims Y" (because there does exist a relationship between X and Y). It would become a stronger argument in the case that X itself can be demonstrated to be false, because it then switches to an argument that the same factors that made A wrong on X make A more likely to be wrong on Y.