Yeah, tidal forces make a measurable difference between the guy on a planet
and the accelerating elevator guy. Basically a planet is (more or less)
spherical, so the gravity field isn't uniform over the flat floor of hte
elevator, but pulls slightly towards the centre of the sphere. With
sensitive enough instruments you could tell that two objects falling on
either side of the elevator aren't moving along parallel courses, and hence
tell the two cases apart.

The equivalence principle also assumes that gravitational and inertial mass
are the same, which (although accurate to a very high degree) may turn out
to not be exactly identical. (See the works of E.E. "Doc" Smith for what
that would mean!)

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