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.
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