The hotel says it didn't get my room request. Why?

The reason why Disney Cast Members say "we don't receive/honor/recognize requests" is to deflect responsibility when they can't give you the room you want. 

If the Cast Member had said "Yes, we got your request," where does the Cast Member think the conversation is going to go from there?

The best possible outcome for that Cast Member is that he or she would have had to explain the process by which rooms are assigned, and why your request couldn't be filled. That takes time, and you'd have the opportunity to critique that reasoning as it's explained to you. 

From the CM's perspective, worse outcomes are possible, too: guests screaming about how much money they paid and/or demanding free upgrades are probably regular occurrences at every Disney hotel. And it's exceptionally unlikely they'd say something like, "We just didn't understand what you wanted," even if it was true; there's no recovering from that.

So any conversation the CM starts with the words "Yes, we got your request..." is a no-win situation for the CM. The easiest thing to do is to blame someone who isn't present. The CM's statement about requests isn't true, of course, but it solved the immediate problem - you went away dissatisfied with us and not Disney. That's why you heard what you did.