Rigid bodies do in fact feel atmospheric pressure. They just have an internal pressure that is sufficient to hold their shape. An example that would be similar are deep sea fish. The pressure in the ocean is very very strong, so the fish have to have high internal pressures to cope. It looks like they don't feel the pressure around them. If you bring them up to the surface where the pressure is less, they burst because their internal pressure is too high. The short version of this answer is: everything feels atmospheric pressure, but anything that is rigid is just strong enough to resist it.