So just to be clear, I know this. I'm not acting like the government did something illegal, I'm acting like someone told me a crime is being investigated necessarily because the FBI is doing the investigating. No shit, dude, I know what the FBI does.
If someone asks for a source when you say the FBI is investigating a crime, they're not asking what the FBI is, they're asking what the (potential) crime is. If you don't know, don't answer; certainly don't answer with something you know is unhelpful. Answering like that makes it seem like you think they're investigating because they can, not because they should.
So, to clarify with this particular case, they're investigating assaults that occurred at the protest, which they should do because that's a crime (and trying to tie it to aNtIfA because they're morons, assuming it isn't malice). One should not trust that the FBI are working within the bounds of the law, one should verify that they are. Hope that helps.