I don't think this is a case of ignorance of a player's status.

As I understand it, the QFA checked Emerson's status and found that he was eligible to play for Qatar. The reason he appeared to be eligible is because he had fake documentation.

So should football associations be held accountable for an illegal act committed by the player? Should they not only be responsible for checking documentation, but also checking the authenticity of it?

This is why FIFA should release a full statement about the incident, so everyone understands why the QFA were not held accountable.