I am perfectly willing to accept proof that I am wrong, however, all you've done is talk without giving any sources or support beyond a vague reference to "ninth grade physics or something like that".
This isn't a political even which means you need actual substance to back up your claims. So please, show me the the math.
Now, here's my argument: words and sound are vocalized as 'packets' of information, meaning that each word is compartmentalized by the silence that precedes and proceeds it. Within this wave packet are the pressure waves that we identify as words. The pattern of the individual waves determines the word we hear however, these patterns are also subject to their component frequencies, which we then identify as high or low pitch.
Now, as for changing the pitch, there are two options. The first is to simply compress or stretch the the whole word packet, which will change the frequency and the time taken to vocalize the packet. The second option is to change the frequency that creates the pattern packet, which does not change the time needed to play the whole sound packet.
(This explanation may be slightly off, as my knowledge of wave packets comes mostly from relativistic physics and probability curves for finding particles such as photons.)
For an explanation that is more easily explained, consider playing a song on a guitar vs ukulele. Both instruments can play the same song at the same tempo, yet the former will be much deeper than the latter. Why? In the case of stringed instruments it is due to the length of their strings. Similarly, one sees parallels in human vocal chords, particularly between those of children and adults and also males and females. Important to note, smaller vocal chords will change frequency one speaks in, but not how fast one speaks.