It’s not really different than other companies outside of astronauts and some people working in, say, educational outreach. For the vast number of employees, there’s no sort of restrictions or even discussions about what’s said outside of the legal concerns (e.g., using NASA titles to convey a position of agency, Hatch act, etc.)

The real mistake here is was made by a potential intern who was not yet hired. It’s like making a mistake on probation, you likely have very little recourse. It’s completely different for regular civilian employees