I really don’t understand how they’re gonna be able to restrict the model access to foreigners in the United States. Employers don’t necessarily actively know who’s a citizen who isn’t.
I think they might still have to mention that they are not a US Citizen as a box on the i9 form, but most US employers are not going to ask any more questions as asking questions about an employees citizenship after they have already provided work authorization is just likely to get you sued as there is not legitimate work purpose. Kind of like how HR is never going to ask you your religion etc. Again this is only very limited information at time of hire and is not tracked or updated beyond date of hire.
Unless they have government contracts, most employers are not actively tracking employee citizenship status.