They have been involved in pretty much all previous USA "idiotic wars of aggression", so while it may become useful in the future to make a distinction, it's also fair to appreciate that this distinction doesn't make a lot sense to a whole bunch of people.
The one time NATO was called on to defend a member was the U.S. asking for help after 9/11. And nobody but the UK followed them into Iraq, shortly after the Afghanistan war began. So there’s certainly strong history of NATO not just doing whatever the U.S. is up to.
I recall this time as a very strong refusal of the above miscategorization of NATO. Bush and his cronies had a whole “you’re with us or against us” tantrum when NATO didn’t follow. I think Americans even did some proto-Trump trolling with “freedom fries” and other nonsense.