My experience with those two streaming services is quite the opposite:
I feed my DAC via USB from my MacBook Pro &/or wireless via Apple TV & to save on HDD space, I don’t even download the music; just stream - whether from Amazon Music App or iTunes. Listening to Apple Music from iTunes is clearly superior to Amazon Music streaming from Amazon Music App. At least that's the case for me & my ears & system; I guess ‘YMMV’ applies.
I have also found Apple Music to sound quite good when streaming directly from my Apple TV feeding my DAC via HDMI; in fact almost on par, if not better than from my MacBook. My guess is there is less noise or less jitter.
I don’t really have a preference to either interface; both are adequately convenient and relatively user friendly. But I also do not have very high expectations on sound quality from streaming from either of those formats, especially after my recent discovery. (Digital audio can sound astounding from plain old Redbook CD’s when implemented correctly. Namely utilizing a separate dedicated CD transport & DAC) - But, I digress; that’s another story altogether, not really applicable here.
“. . . Is there any actual reason for this to be true?. . .”
My guess is there are other factors in play; maybe the source component & the DAC or everything in between. Without knowing a little more about your system components, it would be hard to say.