Part of the acrimony in discussions of AMS is due to a simple issue: AMS is very broadly defined. Some people subconsciously think of the serious issues like HAPE and HACE, and those indeed may have no tie to one's physical conditioning.
But if a person reports of being out-of-breath at altitude, feeling ill after pushing too hard, is that AMS? Medscape vaguely says, "Altitude illness refers to a group of syndromes that result from hypoxia." If your muscles can use oxygen more efficiently, you are less likely to suffer some effects of apoxia, barring HAPE and HACE. After you get in shape, you may try to push harder, and eventually come up to the same barrier.
I see people at the gym or track who get sick simply because they push too hard.