The specific mechanics behind why are never stated that I remember, but there are several pieces of information that combined seem to confirm the statement:
- A morph cannot be acquired from someone else's morph, you need the original DNA.
- You cannot morph from one animal to another without going through your base form.
- Morphs are not physiologically identical to the original animal - modifications are made by the Escafil device to support thought-speak, and the ability to return to your original form still exists (your DNA is stored somewhere accessible and demorphing is triggered by thought).
- Tobias still retained thought-speak during the interim after being trapped in morph and before the Ellimist intervened.
- The Escafil device does not modify DNA, it is technology. Otherwise those who have morphed into each other (in particular, Tobias to Ax) could morph again.
- Loren was able to acquire Tobias late in the series.
These would seem to indicate that a nothlit's "base form" is still their original body, it has just become inaccessible. The body they become trapped in still has the abilities and limitations of any morph, because that is how that body came into existence: The Escafil device won't work on it, they retain thought-speak, and can't be acquired for someone else to morph into.1
When the Ellimist gave back Tobias his ability to morph in The Change, he seems to have done it by resetting Tobias's current form and turning it into an almost normal, non-morph body with thought-speak. He then gave Tobias the ability to morph, as though he was a hawk that touched the Escafil device (like the ant and buffalo in The Hidden). This "reset" also explains why Loren and the auxiliary Animorphs could acquire Tobias.
After that point, if Tobias decided to morph human and become a nothlit again, the Escafil device would not work on his human body the same way it would not have worked on his hawk body previously.
1 Within books 2-13, everyone had their own bird morph, so I don't think anyone tried to acquire Tobias's hawk body. So while there's no proof of this, I don't think it's contradicted either.