I'd guess that interaction is very common and not illegal anywhere I'm aware of.
I'm not a lawyer but I think they're taking a serious risk.
ADDED: As others have noted, there are probably legal issues with that entity effectively acting a full-time employee. And, of course, the entity doing the work can't get any employee benefits.
Its a BILLION dollar industry calling elderly US population from call centers in Tel Aviv, which may or may not have also ties to Niger.
its BIG.
I mean it seems like a ridiculous way of getting work done, but fundamentally possible.
What could work is a middle man (ala upwork), but then you'd have to accept the middle man knowing you.