I am not sure if one race is always tied to one plane. I am asking similar question in another thread.
http://www.enworld.org/forum/showthread.php?t=239142
3.5e introduced the concept of Native Outsider. In case of half-breed or "ancestor is outsider" races, we can safely say their blood of material plane creature is stronger and thus they are native to material plane. But other Native Outsiders like Rakshasa confuses me. They are originally from some other plane but now settled long enough to be considered as a native outsider. That means, a race's native plane may change by time.
Another example is Githyanki and Githzerai. They were not originally from Astral Plane nor Limbo. Also, MoP shows many creatures usually seen in material plane as the resident of certain non-material plane. And, some "any good" celestials can be seen in various upper planes.
Also, there are outsiders like Mercane, which has no native plane written in their entry.
So it is unclear if one race is always tied to a certain plane.
If one race's natural plane change by time, it is possible that human race living generations in Sigil may have Outlands as their home plane. And one race may have more than one planes as their home planes. I mean, it is like sub-race. Mainstream of human are native to material plane. But there are, say, "Outlands" version of human and such.
If a cosmology has more than one material plane, it will become much obvious. Most major races and animals may be seen in each of the material planes. And they have their own material plane as their native plane.
As the rule does not clearlly difine this issue, it is up to the DM ultimately, I guess.