As a general rule, yes the fare buckets are nested.
Even selling an F seat can knock P and R down a seat. It's Yield Management (YM) in its simplest form. The sale of an F fare indicates a demand for F on that particular flight. If paid F is in demand, then why hand out another P or R upgrade ?

That's the immediate effect. Afterwards, YM will follow-up and may readjust P and maybe R back up by that one seat.
High level logic & an over simplified example ...
based on history, YM thinks 6 F seats will go unsold. So it starts selling the flight at F9 P6 R5
The 9 in F9 being the max number displayed (in some cases, IE: partner flights, the max could be 7 or 4 or ??)
Internally, the F9 displayed might be F16 (737-800). Selling an F seat could behave differently when the internal number is F16 vs F9.
If selling the F seat initially lowers P/R by one seat, YM analysis later on may say: "no, that's one of the 10 seats I expected to sell, I still expect 6 F-class seats to remain open, so restore availability to P6 R5.

On the other hand, if YM thinks it's already sold the 10 expected F seats, thus the current sale is unexpected, then the upgrade buckets will remain at P5 R4.

And many folks don't realize that YM is dynamic. That unexpected sale might make YM think more unexpected sales are around the corner thus lower P/R by more than the one seat sold. Initially, YM thot all but 6 F seats would be sold, but that initial thot is NOT set in stone. That initial availability will go up and down as YM evaluates/re-evaluates 1000s of variables.