Yes. Imagine a chair with one pair of diagonally opposite legs very long and the other pair of legs very short. On even a flat surface it is impossible to touch all four legs to the floor simultaneously.

Not even, but the feet have to be coplanar.

And since the spacing between the feet is obviously irrelevant, that further implies that it's always possible to find 4 coplanar points on the surface arbitrarily close together. Or arbitrarily far apart.