The best answer would be Kelley thought the emails were from an anonymous stalker uninvolved with and perhaps even unknown by Petraeus...or perhaps she suspected Petraeus' wife.
Kelley was also a good friend with Petraeus’s wife so why would she turn the FBI onto Petraeus’s wife? If Kelley thought it was his wife, she would have at least showed or told Petraeus about the email and let him figure it out and take care of it. I’m mean we are talking about the soldier/General of the century here, not a whuss!