No. I do not (“have to select”, that is…). I must click.
Secondly, the note value of the button I click doesn’t have to be necessarily larger. It can also be smaller (…for the selected note to change into another value).
You must click a button whose note value is different than the one currently active.
Yes, but in defense of the manual I would say that you omitted to take into account an important part which is the prerequisite, thus required for what you highlighted:
In this context you must select a note value larger than the current note value displayed in the score depending on Display Quantize setting, and which therefore does not reflect its real MIDI value. Because any smaller value will have no effect.