Ohmygod, it thinks these .c files are Intel Assembly, wth.
I'm guessing that because Document -> Select Mode has (Intel Assembly) in parens in the menu. On the new .c file, it says (C/C++).
Lessee, the language manager General tab under C/C++ (Tools -> Options...->Languages->C/C++->General) shows that .c is still assigned to C/C++.
ZOMG, that new .c file, from the template, I just saved it, and now it's got a freakin' third method of doing tabs!
It inserts the closing brace when I type an opening one, but when I do tab, I get this:
hello()
{
(tab)some text
}
So I now have two different methods of tabbing, depending on whether a new c file's buffer has been saved or not (!!!)
And the after-save is, of course, the wrong one.

ETA: After saving the new buffer, the Document menu says Select Mode(C/C++), so at least it hasn't changed its interpretation to Intel Assembly.
Ok, this one problematic .c file does indeed have a tiny, 2-line asm() chunk in it (amongst a thousand C lines), but still, so what? Isn't it the extension that determines how SlickEdit interprets things?
And what about already-existing or newly saved .c files without asm() in them? They exhibit the wrong, 3rd type of behavior, still.
It seems like only a "new" file, created from the C/C++ template via File->New, exhibits the correct behavior,
and that only before saving it!