Except the Rule of Common Sense, which says that if you use the same password for everything, anyone who figures out your password will have the keys to your entire kingdom ...
Your Apple ID and its associated password work for (among other things) iCloud Mail, syncing, the various Apple media stores, the Mac and iOS App Stores, Find My iPhone, iTunes Radio, iTunes Match, and more. That is one password that should be strong (as we've all learned this week) and best preserved in iCloud Keychain so you don't have to try and memorize it.
In this specific case, I believe you happened to access the Apple TV during a period where Apple was having iCloud issues. The problem persisted for about 5.5 hours, but not all users were affected (I was aware of the outage but it did not affect me at all). Once the outage passed, your old password was probably restored.
Apple had another such outage today for about 3.5 hours. Again, I checked with colleagues across the US and none of them were affected, by the system status page doesn't lie.