If Broadwell sent the harassing communications from the same gmail.com account she used to communicate with Petraeus, well, “stupid” comes to mind, unless she intended to associate Petraeus with the harassment, along with herself.
I don’t think she is that stupid. Presumably the FBI tracked her IP addresses and got a court order for all her other email accounts. Or maybe the whole FBI story is a fairy tale. Who knows at this point.
If I have the FBI involvement correct, it makes sense, and was a sort of "favor for a friend," thing. Kelly mentioned the harassing e-mails to a friend who is an FBI agent. This is the agent who sent the shirtless pics to Kelly, but before this harassing e-mail issue surfaced. The FBI has jurisdiction and authority under federal law to investigate and prosecute cyberstalking. No that they spend big chunks of resources on this, but at least it's work they are supposed to be doing.
I figure Broadwell tried to hide her ID (and didn't use the gmail.com account shared with Petraeus to originate the harassing communications), but left enough of a trail that investigators could get back to her as the sender. At that point, they are investigating Broadwell. They already have whatever court orders are necessary to investigate HER for violations of federal law, so sweeping all of her e-mail into view is natural. That's when Petraeus came into view.