No, you have that wrong. The opposite of "fee-only" is "commissioned-based" - where you don't have transparency into the cost of the advice (which is free at the point it's offered) because it's kicked-back to the advisor by the funds etc. that are being offered.

A fee based on AUM is an entirely standard way of paying a fee-only adviser.

ref. https://www.napfa.org/financial-planning/what-is-fee-only-ad...