OK. It would seem that I am in agreement with you. For the most part. On the full scale side though there have been great strides forward in the overall classification of GT cars World wide which opens the door for the droopers among us that think a Civic with a venetian blind wing on it is a viable as well as beautiful "GT" car because they compete in the JTCG or whatever it is as opposed to the old yet still widely accepted GT standard for the US or the European versions of GT cars that are produced over there. The Datsun example you presented(very nice by the way) was a "C" production car that competed in the SCCA. It wasn't until IMSA came along that it was recognized as a GTU car since it fit in the under 2.5 liter requirement of the day.
It isn't my choice but if it were I think I could fix it by simply stating that USGT stands for GT cars that have competed or are competing in a GT class here in the US. In other words if you don't see it competing in a televised series on American soil then you can't run it in any "officially" sanctioned USGT race. As always, track operators have the final say for their own facilities as long as it isn't a sanctioned event.
As for the tires, since there is no way to enforce the insert rule, I don't think requiring tires for sanctioned events to be purchased at the event is unreasonable. I understand the cosmetics aspect but if you watch a televised event you will be hard pressed to find an assortment of cosmetically pleasing wheels throughout the field.