The linguistic proxy for pitch is tone. As far as I know there are no languages where a tone distinction is not at all implemented via F0 differences, but there are very many where the distinction includes things other than F0. The best-known examples of that are SE Asian tone languages like Vietnamese, where tonal differences involve amplitude, phonation and durational properties (sometimes vowel place distinctions) as well as F0 differences. In some languages such as the Western Nilotic ones, fully phonemic phonation distinction is an autonomous and orthogonal vowel property, and in those language they do not (by tradition) call the breathy / modal distinction a "tone" difference, whereas the SE Asian bundle of properties is just called "tone" (there is also mention of "register" in the literature). Phonatory concomitants are probably the most common, though they are under-reported since F0 is trivial to detect and report, and is most salient in perception.
The question about speakers perceiving a tone as rising is an instance of a pretty common fact about people who speak tone languages, that they don't use technical linguistic terms the way we do (and more often, they use other terms). I have found, in a number of African languages, that when speakers "discover" a contrastive parameter of their language via a minimal pair, they will often say that you "drag" one of the vowels (I've found little consistency in what "drag" means). Or they might say that a vowel is "light" (or "heavy"). I have never heard a speaker spontaneously refer to something as "rising" although one guy (not an average Joe) did learn what "downstep" and "fall" referred to. In other words, naively used terminology is usually incorrect, anyhow. Given that caveat, it is nearly universal that people's beliefs about the F0 path of a given vowel are incorrect to some extent.