The constant pressure is mostly crap!
Every gas contracts and expands with changes in temperature, and nitrogen is no exception. There is, however, one way that this can be true.
If the air in the tire is high in moisture content, than this moisture can evaporate into steam, or condense into water with changes in temperature. Under standard temperature and pressure, 18g of water makes 22.4L of steam, so its a fairly sizable difference. However, this difference starts getting negated quickly
1. Since the tires are pressurized, it takes a pretty damn high temperature to turn water into steam, much more than the standard 100C.
2. Only a very small percentage of the air is water
3. Most of the water in the air gets left in the bottom of the compressor tank
4. Many compressors have driers on them to take care of this extra moisture.
But really, its a damn sales gimmick, trying to stiff you for a few more bucks. It may make sense in professional racing, because its one less variable to worry about and whats a few more bucks when you have a couple of thouthand in even a crappy race team, but it makes no sense what so ever for the average roadracer.
As for the tire, take a picture from the back, so we can get a better idea.
Or, get a few friends, and ask them to lean the bike over (it will take at least two) while you stand behind and watch. Ask them to lean it over as far as they can, slowly, while you see which part of the tire contacts the ground. You will be able to see what the max lean angle the tires can support, it wont be as much as a sport tire, but believe me, it is waaaay out there, and I seriously doubt you are hitting it.
However, you can loose traction way before you run out of tread.