Does an Outsider gain the Native subtype while on its home plane, and if so, what does that mean, exactly?
The confusion comes from the word "Native", which is a bit misleading. The description is:
This subtype is applied only to outsiders. These creatures have mortal ancestors or a strong connection to the Material Plane and can be raised, reincarnated, or resurrected just as other living creatures can be. Creatures with this subtype are native to the Material Plane. Unlike true outsiders, native outsiders need to eat and sleep.
So "Native" means "Native of the material plane" rather than "Native from the current plane". As the Material plane works differently than outside planes, Native Outsiders are somehow "less Outsiders" than "real Outsiders".
An Outsider not from the Material Plane would then not get the Native subtype while on its home plane.