The elevator car is a thought experiment that draws attention to the equivalence in sensation of acceleration on one hand, and being in a uniform gravitational field on the other hand. As you correctly point out, this particular thought experiment breaks down when you consider that all of the gravitational fields that we are accustomed to are non-uniform, and have apparent tidal forces.
The real principle of relativity is a bit more subtle (sometimes called the strong principle): that the effects of gravity can be explained entirely at the level of local geometry, without any need for non-local interaction from the distant body that is generating the gravitational field. To describe the geometry of non-uniform fields, we need more sophisticated mathematical machinery than what is implied by the elevator car thought experiment, but nonetheless, the elevator example is a useful launching point for that type of inquiry.
The real principle of relativity is a bit more subtle (sometimes called the strong principle): that the effects of gravity can be explained entirely at the level of local geometry, without any need for non-local interaction from the distant body that is generating the gravitational field. To describe the geometry of non-uniform fields, we need more sophisticated mathematical machinery than what is implied by the elevator car thought experiment, but nonetheless, the elevator example is a useful launching point for that type of inquiry.