Setting aside Printz v. United States, in general any law enforcement officer has the authority to enforce law at any government level if they see a crime taking place. An FBI agent has the legal authority to arrest, cuff, and detain a mugger when he sees the crime, hold the perp, and then turn him over to local PD when they arrive.
You, private citizen, do not – even with your awesome "citizen's arrest" authority
Imagine the outcry if that FBI agent
had to stand there 10ft away and do nothing. He was interviewed, and it was all over the news. Not allowed to intervene, by law. Stated he really wanted to help the old lady, but all he was allowed to do was call 911.