A significant amount of rocket technology is covered by ITAR (International Traffic in Arms Regulations), which means that its restricted to largely US citizens. That means it cannot be legally shared with foreign college students, for example.
The first rockets were basically ICBMs without the warhead. Gemini capsules were launched from a Titan II rocket, for example.
I should have said "US Persons" not "US Citizen" above.
I'm not sure about SpaceX specifically, but if you were a Green Card holder. e.g O-1 Exceptional Ability, then you'd be considered a US Person for ITAR compliance.
From http://www.spacex.com/careers.php
"To conform to U.S. Government space technology export regulations, applicant must be a U.S. citizen, lawful permanent resident of the U.S., protected individual as defined by 8 U.S.C. 1324b(a)(3), or eligible to obtain the required authorizations from the U.S. Department of State."
It doesn't sound like SpaceX require a Secret/Top Secret clearance for most of their employees. Some other space companies (Orbital Science Corp, ULA/Boeing/Lockheed Martin) do because they work on missile systems like ICBMs in related programs.
From what I understood, most engineers who make the grade to work at SpaceX, would be O-1 visa eligible as well. The O-1 is not tied to continued employment at a particular company.