Is it bad to mix different size tires on a car?

I tried to buy ONE tire to replace a cut tire on my Neon, and they refused to install it on the front.

I could have them install on the rear, leave and come right back, and have them rotate to the front, but direct install? No.

Their concern was new tires in the front could grip more than worn tires on the rear resulting in accidental oversteer which could cause a wreck.

I went elsewhere for the tire and have yet to crash the car.