The potential energy has a gauge freedom, that is we can define the zero to be anywhere we want without affecting the physics. A side effect of this is that we cannot experimentally measure potential energy, we can only measure differences in potential energy.
So when you say the potential energy of an object raised to a height $h$ is $mgh$, what this really means is that raising an object by a distance $h$ changes the potential energy by $mgh$ i.e. the difference in the potential energy before and after raising was $mgh$.
The person holding the suitcase can define its potential energy to be zero, but this is just a choice of gauge. Regardless of how the person holding the suitcase defines the potential energy it still changes by $+mgh$ when it is raised by a distance $h$ and $-mgh$ if it is lowered by a distance $h$.