I tried it with an official IDPA box, and the spacers that IDPA sent to the club.
It fits fine, and the lid closes completely. With the tolerance specs, I have no doubt that you could hold the lid closed if a box was tighter. The tolerance is that the box can be only 1/16" larger than any dimension, there is no acceptable tolerance difference on the lower side.
The lid is a little wonky, but I flipped it around with the levers inside and it looked the same.
