Yeah, I find it pretty absurd that would cause gearbox damage. Aftermarket wheels and tires are one of the most common things done to exotics cars. The car should have a lot more than fine print if something as serious as damage to the gearbox can occur with such a change. If word got out that such a minor change to wheels on an exotic could cause serious damage, that car would probably be lambasted on all the forums and press.
If the difference is as you say, a mere 9mm, that makes it even more absurd. As you said, something like general wear and different pressures could make a change in rolling radius.
I they haven't already flagged the car or voided the warranty at your current shop, you should swap your wheels/tires to stock and ship it elsewhere. It might be a pain in the ass, but worth it if they are giving you such a hard time.
BTW, what are the specs of the other stock wheel styles as well as snow tires? Are they all exactly the same?