What is it we have lost sight of?
We seem to be going quite far afield of the actual incident in question to slag on the authorities for looking into his flight.
His innocence, from what we know, was never questioned. No charges were brought or discussed. He didn't mention any discussion of possible violations of the law by the FBI.
He flew near an Air Force base, something that I assume happens all the time, but this time there was reason to investigate and determine who it was, and have a chat with them. The resources expended here were significant, mostly in tracking him down, and given the delay it seems it may have taken some effort.
So it's a fair assumption there was a compelling reason to look into THIS flight and get details on who they were and why they were there. Likely a sensitive reason that, as such, we'll never have a clue about, including the OP.
I have no problem with that at all. I have a problem with such authority being abused, which doesn't sound like it in this case.