The time I had an engine failure (and made it back to the runway) flying young eagles, the airport manager called the police, fire, and FAA, as well as stealing a gallon of fuel from my plane for "testing purposes" (though it was clear this wasn't a fuel problem). The only person who DID NOT respond was the FAA. Some ultralighter killed himself two counties over and since mine wasn't really a reportable accident and nobody was injured, they didn't care. The mechanics moved the plane into my tie down while I dealt with the police and the field was opened again.
I avoid calling the FAA on my field. Sometimes, they find out about it anyhow. I got a call while I was at Oshkosh first from the local TRACON asking about the gear up on my field. Told him I was standing in Oshkosh at the time, but I would check it out. Turns out an MU-2 on a flight plan had done so. Nice thing about bullying in an MU-2 is it does minimal damage. By the time I got a hold of someone back home (who wasn't at Oshkosh) a bunch of neighbors had got the thing back on it's wheels and pulled off the runway. The next call was from the FSDO and they weren't as kind (especially when they heard the plane was moved). I told them there wasn't much I could do from 700 miles away.
Of course, there was the time a plane didn't run off the runway, didn't go down the embankment, didn't end up in the yard across the street. A bunch of folks didn't pick it up and put it on a trailer and didn't push it into the owner's hangar. I didn't get a call from the FAA on that one (though my wife did in her role as president of the HOA).