God. Some of you guys really have to stop playing Skyrim...
In real life, Dogs nudge against you for attention and affection. This isn't a strange bug or glitch. It's a realistic behavior.
Yeah, sorry, even with my cousin's great dane, he doesn't nudge me so hard it shoves me 5 inches.
Honestly, OP, here's how I see it: You can not force an NPC to move by walking into them (you can get up in their face, and they'll sometimes step back if you do, but that's not the same mechanic here. We're talking about being able to push the identity around.)
NPCs, for whatever reason, force you to move when they want to get somewhere.
This is an inconsistency in behavior and mechanics; therefor, I deem it a glitch. Unless someone can show an official statement deeming it to the contrary, I'd operate under that logic because, well, it's a conclusion came upon with basic logic. There's dying from incompetency, and dying due to pure bull-[censored] -- what you experienced was pure bull-[censored].
My two cents.