They had troops in Iraq from 2004, and I participated in an anti-NATO protest in London that year. Citizens of the NATO alliance demanded withdrawal, but the details seems to change over time.

Not every NATO member agreed to the invasion, and Sarkozy and Putin held a press conference together to detest the invasion. It's hard to imagine this today, but it happened.

If I punch someone in the face but don't officially declare I punched someone in the face, did I punch someone in the face?

Iraqis didn't want NATO or any foreign troops in their country; is their presence an invasion?