>Do the local police have that authority over the FBI in the US?
The FBI, even if it had jurisdiction, would usually play a supportive role. The FBI has to work with local police all the time and hesitates to through its weight around unnecessarily. In a situation like this, the FBI would provide a agent as a person to contact if the BPD wanted anything and would offer technical equipment for phone taps, agents to man the tape if needed, they would have 'beeped' a few agents to be on standby such as a low-altitude surveillance pilot, they would have offered the services of their crime lab (though thats a bit of a joke, these days especially).

There is a 'presumption' that a kidnap victim has been taken across a state line and thus the FBI has jurisdiction, but once a supposed kidnap victim is found in the house, then there is no presumption of interstate involvement and the FBI's jurisdiction would evaporate.

Sure, if the FBI agent had really been alert and aggressive he could have said this is a 'terrorist threat involving a subsidiary of a defense contractor' but the FBI has no desire to ruffle the feathers of the local cops.

In the JBR case, the FBI's response seems somewhat minimal and half-hearted.