Lots of space technology is classified as weapons subject to export control. ITAR has plenty of rules about who can see information. US immigration status generally has to be green card or citizen, and country of origin and any second citizenships are considered.
("export control" in this sense really doesn't have to do with moving a physical object out of the country but sharing information, to the extent that a conversation in an elevator could be an export violation. most export violations amount to emails being sent to the wrong person)
When I worked briefly in defense, for example, there would be regular random searches of my stuff as I exited the building and security would wander the building and look at what you left out on your desk while you went to lunch. Entirely seriously they told us not to wear our badge in public if we left the building and not to leave our laptops in our cars because someone might follow us and steal it. Had colleagues who were visiting a foreign country for work have their hotel rooms obviously thoroughly and messily searched while they were out.
They also do national security missions so there are folks there with high clearances.
Thing is that even if you did steal a bunch of information, that doesn't mean you could just copy and be successful. Any one of a million things can go wrong with a self-landing rocket that will cause it to explode, you can't just steal the whole system of operation that keeps these things from happening.
You couldn't steal all of the secrets of a circus performer and suddenly be able to juggle chainsaws while riding a unicycle.