The FAR's permit operation of their a/c in a foreign country by a licence holder in that country type-rated on the a/c. That's fact, but now from memory, I think it's only for Private ops.
So, I could buy a US registered a/c and operate it here privately with no problem. THE problem is that it's annual and/or repair work MUST be done at an FAA licensed Repair Station.
They can be hard to find an expensive in some cases.
You'd have to talk to CASA about doing it commercially.
G'day
Oh, and if the Panther PA-31 driver's qualifications bother you, for the operation of that a/c, he has US ATR, I/R & CFI.
