I used to work at a CostCo garage.
The different attitudes you guys are getting about upsizing tires are a direct result of the manager's outlook.
My manager was into offroading, and he would let the guys put any tire on any vehicle that the customer asked for. (To a reasonable limit of course.)
If we thought the tires would rub, or just wouldn't fit at all, we would tell the customer that, we would write it on the invoice saying "TIRE SIZE NOT ADVISED BY INSTALLERS" or something to that effect. And the customer had to initial that statement also.
The corporate policy though, is to not install tires with a greater than 3% overall diameter different than what the car came with from the factory. There is a program in the shop computer that lists all OE sizes and they also have a 2nd program that compares one size to another and gives the % difference between the two sizes.
You have to remember the liability side of things, if someone comes in, gets larger tires and they go out and flip their vehicle, they can come back and try to sue the store that put them on.
CostCo is a huge corporation, and they are just trying to limit their exposure to possible liability as much as they can.
And has been mentioned, to easily get around this, you can just bring in your wheels and they will mount the tires on them and you can take them home and bolt them onto your vehicle. They will do this with little to no questions.
CostCo also has (or had when I worked there) a policy of lifetime flat repairs, mounting and balancing on tires they sell. The limit on flat fixes (punctures in the tread only) maxed out at 3 fixes per tire - after that the tire's carcass is considered to have been weakened enough to be considered a safety hazard, and they won't repair the tire a 4th time. They will however pro-rate the tire based on tread life or mileage, and refund a percentage of the original purchase price towards a new replacement tire.
They won't try to repair a sidewall-damaged tire. I haven't run into a reputable shop that will actually work on a sidewall - if they are able to fix the damage, the fix likely won't last too long.