That's completely not the case much of the time. Frequently, non-US-citizen remote people are hired as contractors rather than permenant employees. Otherwise, it gets ridiculous -- I hire a Serbian guy and a Ukrainian guy and a French guy -- that would, under your scenario, require 3 different subsidiaries and all of the bureaucratic nonsense that would entail -- opening a French subsidiary, for exsample would be next to hell in terms of trouble -- especially for an American company with no physical presence in the country. No way. Most companies would never do it that way.
The best and easiest way is to simply hire the "employee" as a consultant/contractor -- then that person can handle taxes/etc however they need to. For example, what if you're a Serbian citizen working remotely from Thailand for a US company while getting paid into an EU bank account?
It gets ridiculous in a hurry -- unless you're paying remote overseas employees as independent contractors.
