Whatever transpired, the FBI agents found no indication that it cons uted a crime or a threat to national security. They confirmed this when they interviewed Broadwell and then Petraeus. They are both said to have been forthcoming and consistent, even telling the agents more than they already knew.
Petraeus seems to have been the first guy in memory not to lie about sex. And a good thing too, because lying to a federal agent is a crime. Martha Stewart found that out the hard way.
By that point, FBI headquarters almost certainly had been notified. One former agent with extensive experience estimates that it would have taken no more than 24 hours for word to get to Director Robert Mueller. A case that might never have been if the agents in Tampa had heeded their initial misgivings now presented the head of the FBI with a predicament in which there were no happy options.
In all electronic surveillance, including emails, the FBI is legally compelled to adhere to the principle of “minimization,” limiting the invasion of privacy as much as possible to what is specifically warranted. This applies even when a case involves the worst kinds of criminals.