That seems incorrect in my case. I have both a recovery key set and a screen time passcode and I can still go through and change the Apple ID password with the procedure you listed. (I just, in fact, actually changed it - and very shortly afterward realized that this meant that my Sonos stopped playing music because I had to reauthorize my Apple Music account.)
Having a screen time passcode with account changes disallowed makes it harder to find the Apple ID address on the device, but not impossible.