I see your point about going undercover. But I think the fact that they said they were with the AP modifies things slightly. If they had pretended to be a reporter from some made-up news agency, then sure, I could see it as "just going undercover". But they used the reputation of the AP to carry that out. It isn't quite impersonation, but it is close. And it potentially harms the credibility of the AP. So, in that sense, it is more than "just going undercover".
It would be interesting to see whether the AP could sue the FBI under the 'takings' clause of the constitution, because the FBI has taken some of their reputation, and harmed the AP's ability to conduct its business.
