C J Campbell wrote:

If the FBO pursued its claim against you, you would be able to sue them
for defamation,

Defamation? Sending you a bill is not defamation, even if they
intentionally sent it to you knowing you weren't responsible for it.

claim damages for fraud,

What fraud?

? and possibly press criminal
charges for conspiracy to defraud you.

Conspiracy to do what?

You need to get your legal theory from someone other than judge judy.