In a indirect way it did, (standing on the shoulders of giants, heritage of the people working there, etc,) however, unlike the other companies you mentioned, SpaceX only hires American citizens (because of government contracts and ITAR.) So it's basically an all-American effort.
I don't work directly with anyone like this but I know SpaceX has a few, not sure of the exact number, employees who are neither citizens nor permanent residents.
From what I've heard the process of getting a non-US person ITAR cleared is extremely costly, both in time and money and is thus used very sparingly.
There are quite a few foreign born American citizens working at SpaceX, myself included. You may find this shocking, but seeing as English wasn't our first language, some of us even have foreign accents.
I don't consider them, or myself, any less American.