A BB shell would have to be super crazy out of whack to bind up a BB. Especially a traditional cup/spindle BB.

Run that fixed cup in by itself. Does go in ok by hand? If not how much effort does it take? Just as the cup flange meets the BB face check for gaps with bright light. You could also mark up the shell face and cup flange with a Sharpie or dry erase marker then lightly seat the cup then remove and check for a wear pattern.

With a Campy cartridge BB its easy to check for BB face alignment. Screw in the Cartridge first, maybe half way in, the screw in the cup. If the cup goes in with minimal effort the BB shell itself is in fairly good alignment. Now fully seat the cartridge. If the face is out of wack the cup will have a hard time tightening down.