Make sense to me. The FBI agent was a friend of Kelley’s too, and I can see her asking the agent for help about these weird threats that she knew to be baseless, rather than embarrassing herself by running to Gen. Petraeus who she obviously held in high esteem.
(Based on everything I’ve read which indicates there was nothing going on between Petraeus and Kelley other than friendship)
She has a very important and supposedly respectable friend, so she asks her FBI friend to look into what nut is sending her kooky email about him.
She didn't want to bother Patreaus with it, because for all she knew, this was completely her problem (stalker nut), not his.