Great perspective, it was not a purely American event. People from around the world participated in this event. From all of the Canadian Avro Arrow engineers that were shipped down to NASA when that project was cancelled to all of the communication outposts around the world then again the German rocket scientists that you could say were kidnapped by the Americans as WWII ended. As I recall from the shades of memory, putting the US flag up was more of a minor part of the whole event as you correctly point out that it was a world event and the moon was not claimed by America as everybody had already decided that no one country can “own” the planets and moons. If someone from another country were on this or subsequent moon landings, they would have planted their flags too.