It was viewed as illegitimate inside the US too. And yeah, I remember, even as a 17yr old at the time, seeing the event happen live and lamenting to my mother that we were going to have another Bush term over it. Historically for America that’s always been the case.
You should read your own link, because it also mentions that by the end of his term, most disapproved. By 2006 it was viewed as illegitimate by most. My recollection of events is fine, thanks.
America will generally approve of measures when they are led to believe it affects their security and safety. It’s the years afterwards that determine if it continues to hold support.