No. Does not make sense. Anyone would call the friend if they were in fact friends. No one would make their first call to the FBI if a friend was involved.
I'm not sure that I would have done differently.
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)