VC dimension of linear separator in 3D
You have a small (but crucial) misunderstanding of what the VC dimension of a class is.

The VC dimension is the maximal number $d$ such that there exists a set of $d$ points that is shattered by the class.
It doesn't mean that every set is shattered. 

In this case, indeed 4 co-planar points cannot be shattered, but if they are placed in a tetraeder then they can be.

This is similar to the case of 2D: 3 points that are co-linear cannot be shattered by a line, but there exists a set of 3 points that can be shattered.