Not sure where the argument is, as she's ex-RCAF Yale 3417, purchased from Ernie Simmons in the late 60's before his death (and was not in the famous 1970 auction) She was initially in Michigan with a couple of different owners as N4737G, and went to Edwin Schnepf/Challenge Publications in 1974 where she was restored as a 'BT-9B' in paint only. Donated to the USAFM circa 1978. The only thing done to her that I can see is that the characteristic carb air scoop at the top of the cowling has been removed and replaced with an ....empty hole

I always get a chuckle at the display...an NA-64 painted as a BT-9 but labeled as a BT-14. Sigh...Unfortunately the NA-64 is essentially a mix of BT-9 and BT-14 components. BT-9 wing and engine with BT-14 fuselage and tail feathers.
Maybe not so much "argument" as "confusion" due to the signage.
I remember seeing her flying on the cover of Air Classics back in the 70s.