> That's how the shell behaves.

Ok.

In this specific case, which is trying to run a program and failing from
inside Emacs, I think it could be argued both ways: that it is more
informative to know there's something a bit off in your PATH, or that it is
irrelevant, because the relevant info is that the program couldn't be run.

I suppose the answer to "one way or the other" is "Yes, as long as it is
consistently done in all platforms."