Ok, so I finally figured out how to reproduce this really easily. As I suspected, it is related to movement, but not in the way that I initially thought.
Here's the best way I know how to describe it:
Sometimes you're running and you want to cast a spell, and you know you need to stop running to cast, so you stop and then begin casting immediately. However, once the spell's casting time is up, it says your spell was interrupted. Now, this generally makes sense, and this is classic as heck - you simply didn't wait long enough before hitting the cast button, and your character was in a sort of "slowing down" from movement phase after you stopped running, thus interrupting the spell.
Well, the same thing applies to hide, except instead of saying "You must be standing perfectly still to hide" and failing, it gives you a successful hide message and puts you into a failed hide mode. I'm going to assume that this is not just a rogue issue, and this can happen to any race/class with the hide ability. It doesn't have anything to do with sneak, even though in the screenshot I've provided it shows me in sneak as well.
Here's how to reproduce the bug: run forward and then stop running, and
immediately after you stop press hide.
Here's a screenshot of me after reproducing the bug. Notice my nameplate does not show me as invisible, and the successful hide and sneak messages show as the most recent entries in the window at the bottom.
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