This page (and I think in a couple other places) it mentions that the maximum PC upgrade is to a Premium class vehicle (G):
https://www.hertz.com/rentacar/ememb...umGoldbenefits So it is good for OP to know this going forward.
But that is as noted a separate issue. The main issue is that yes indeed you can make an F reservation and the location can give you a much higher car class as your vehicle if they feel like it, and no they can't change the rate after the fact. You should have a printout when you left showing the rate you expected and agreed to. That is what you should pay and hold them to it. This particular Hertz location is trying to CYA by pulling this switch. Someone may have to take a fall for it, but there's no way it should be you.
Your point with them is simple. Details of how you came to the arrangement are not particularly relevant. Here's the rate you agreed to and on the contract you "signed" (not really signed each time when you're Gold but for all intents) and when you got back to return the car they pulled a rate change on you. You want the original rate, period.
You didn't return it late did you? Just making sure of that. That would diminish your case a bit because rate changes are possible if your return puts the rental outside the parameters of the original rate.