My guess is this is an example of Hanlon's Razor. A disconnect between their lawyers and their HR staff or hiring managers as to their specific obligations under ITAR would easily explain all of this.

I doubt there was even a specific refugee or asylee actually involved: a poorly-worded job posting would justify this complaint.

If it was most other business owners, I'd probably be a lot more likely to agree with your take regarding potentially doing it for the right reasons (protecting against espionage, sabotage, etc.). Then there is the fact that these are asylees/refugees, which I'd assume wouldn't be hired in a position where espionage, sabotage, etc., are a possibility. Probably more like menial type jobs, away from "innovative technology" and "potential sabotage" positions.

And then there is the following claims from the JD link:

"SpaceX routinely discouraged asylees and refugees from applying and refused to hire or consider them, because of their citizenship status, in violation of the Immigration and Nationality Act" and;

"SpaceX wrongly claimed that under federal regulations known as export control laws, SpaceX could hire only U.S. citizens and lawful permanent residents, sometimes referred to as green card holders. Export control laws impose no such hiring restrictions."

I'm not an attorney, but it seems like all they had to do is not discourage them, at the least, and at the most, just interview but not hire them. Oh, and keep their mouth shut about things they aren't knowledgeable about the law.