While technically, I do think that wheels and suspension parts *could* effect the transmission, I *highly* doubt that is the case - unless you have 50" wheels on the car or something. :-) I *think* that I read somewhere that very large and heavy wheels do make it harder on the transmission, I'm not 100% sure about that - does anyone else know?
Something else to consider - if your wheels/tires are a different overall size than the original wheels - and you didn't have the speedometer re-calibrated for the new size, wouldn't it also impact the mileage that the vehicle reports? Or doesn't it work like that? I'm just wondering if they are trying to say that mileage is so close, that different sized wheels could mean that the warranty is actually exprired already due to the different sized wheels impacting the reported mileage.
Yes, heavier tires and wheels make life harder for the drive train, and the brakes. Plus impact handling negatively. Unsprung, rotating mass is the worst kind of weight on a vehicle.
Are those 22s enough to make the transmission fail prematurely? Most likely not, but it would be interesting to know the tire size.
As far as the speedo maybe not being corrected, that should be a non issue, unless the static loaded radius differs quite a bit between the stock and aftermarket tires. Let's say the car traveled 1,000 miles according to the odometer, but in reality it went 1,050. Well, the transmission doesn't know that. It still thinks it went 1,000, based on the number of revolutions.
Besides, the error must have been there long enough for the odometer to be off by that much, which doesn't seem to be the case.
Then again, some modern vehicles can be finicky about gearing changes, be it through gears or tires. Doesn't sound like that's the issue here, though.