Article doesn't say that was the case in the initial complaint. It just said that chic 1 felt threatened by crazy chic 2 via emails. Unless chic 1 mentioned Petraeus’s name to the FBI upon initial contact, I can't understand why they would get involved.
I'll bet that chics get threatened by crazy chics on a regular basis and the FBI could care less.
Crazy chics making threats to others usually don't entangle the Director of the CIA, if the other woman who was 'close' to Petraeus was professionally or personally associated with him they would possibly fall under the FBI's jurisdiction wrt to threats (federal employee or family). As for looking at his email account during the investigation they would have had to have good reason to look at the CIA director's account, not something you do on a lark.
Edit: This article provides a bit more context of how he got ensnared, they FBI was trying to find out how Broadwell got the email accounts and checked out his account to see if she got them from there.