Your ukulele demonstration made me think of a violin, and I think it may be even more illustrative of the concept. A violinist can move the bow as fast and hard as she wants to, but the pitch won’t change because the thing that determines the pitch is the length of the vibrating medium – in this case, the string. In the case of trumpet playing, the vibrating medium is the lip tissue between the aperture corners. The air is like a violinist’s bow.
I think the misconception stems from an understanding that the medium must vibrate more or less quickly to change pitch, but not understanding the physics of how that does and does not occur, i.e. faster bow/air vs. length of the vibrating medium.
A vibrating medium of a given length will vibrate at the frequency that corresponds to its length, and cannot vibrate at any other frequency. Hitting it harder with faster air results in an increase in the distance of the wave peaks from baseline, but does not shorten the wave (louder, not higher).