Instead of arguing what stores I want to spend a dollar on a battery, I will give my answer to the original poster....
Put the one that it calls for. On a $350 key fob, don't play science experiments with battery sizes... I looked at the 2032s and it was TOO thick... Do you want to risk squeezing the electronics and mechanicals in the FOB just for an ego rush that you put a BETTER battery in..
We do not live in a third world country where we have to adapt everything because of poverty..
1. the thickness difference is 3.2-2.5=0.7 mm
2. The mechanical buttons are not squeezed because the PCB shields it.
3. The only part that is under stress is the PCB board. That PCB board is 0.9 mm thick and pretty strong. It would be interesting to see if there is any statistics about damage caused by the 0.7mm thicker battery.
I agree with you that in general, poor people would like to save money, but since they like to show their status, they may not admit that they like it.