Yes, it's an unwarranted fear. Think of it this way; there's probably no more than a pound or so difference between the lightweight road bike and the heavy mountain bike frames that you're looking at. You can either have big diameter tubes in the frame that look fat and strong, and are the thickness of a Coke can, or you can have smaller diameter tubes that have about the same amount of metal, but they resist denting much better than the empty Coke can.

There are two other reasons for a "leaning-over" bike tjspiel didn't mention. First, by leaning a bit, you can engage your hip and back muscles in pedaling. That lets you ride further, faster, and with fewer aches and pains, than sitting bolt upright. Second, if there are potholes or rough pavement where you live, leaning over lets you absorb some of the shock from riding over them with your arms and shoulders, rather than feeling 100% of that shock in your tush.

When you go back to the shop, arrange to take a 1-3 mile test ride on all the models that interest you. Ask them where to ride; if it's a good shop, they'll hold a credit card or driver's license and give you directions. (I caused near panic when I bought a bike from REI. Only my daughter's continued presence kept them from calling the cops to look for me!)