Yes you are correct. On a legal RNAV approach, you can’t alter or fly direct to any fix beyond the FAF. There’s a good reason why. Because that’s the whole purpose of the approach being built is obstacle clearance. You fly direct to the MAP does not guarantee you clearing the trees/towers/mountains, legally speaking.
For extra credit, you mentioned that ATC can have you direct to an intermediate fix, however on RNAV RNP approaches, you have to be careful because those fixes may be fixes that the AP can’t turn tight enough to rejoin the approach. Airbus has this limitation.