Brad, foreign teachers with BA routinely get F visa from this agent. It is illegal to work and get paid by a school on such a visa as it is a business visa. Short term lecturers may get away, although contracted teachers, who are in for the whole semesters, may more likely get in trouble. It surely depends on the school's relationship with the local authorities, but the point is that this agent acts as an escort service catering local employers that often do not have a license to hire foreign teachers. Moreover, the issue is that the agent takes a share from those employers who take it out of the foreign teachers salaries. Whenever problems in between employers and teachers arise, you know who will wash his/her hands of first.

Cheers and beers