On the contrary, I'd be perfectly content classifying our probing of gravity/acceleration indirect, too. For completeness I include gravity because it's the only other fundamental interaction we arguably directly sense (inner ear fluid and fine hairs are part of the same sensory organ, unlike our skin and the sun).

But I still suspect we would be able to sense gravity without inner ear fluid, even if only slightly. When we vigorously shake our head, the fluid flows against the hairs, so naturally the electromagnetic force and/or Pauli exclusion is mostly responsible for sensing. However, even absent any inner ear fluid, the hairs should still bend due to gravity -- I just don't know how appreciable the effect is.