Clearly it will fail given a big enough lift to experiment in, since a big enough lift would essentially include whatever object is creating that gravitational pull (or enough to conclude its existence from other phenomena). However these effects are nonlocal, you need two different points of reference for them to work (like your two baseballs). In fact most Tidal forces are almost by definition nonlocal.
The precise definition involves describing curved spacetime and geodesics, but that one is really hard to visualize as a thought experiment. The thought experiment does offer insight though, as it is possible to imagine that, absent significant local variations in gravity, you cannot distinguish between free-fall and a (classical) inertial frame of reference without gravity. This insight provides the missing link that allows you to combine gravity with the laws of special relativity and therefore electromechanics, including the way light bends around heavy objects, which provided one of the first confirmations of this theory.