CL, the local employers' liability over foreign teachers' health checks is a rather interesting concept. For the sake of this topic, THE HEALTH EXAMINATION CAN BE FOR 6 MONTHS ALTHOUGH THE RP FOR ONE YEAR. Further more, more and more foreigners get their health examination done on their own either mainland or at home and they pay for it as well. Then, they submit their Residency Permit applications alongside other documentation necessary with the schools' reps at the PSB. Your claim that the health check has to be for the same period of time as the work permit is wrong as some areas in the country practice their regulations differently. For example, Chongqing issues only 6 month health certification, but fts get one year work permits with it. Keep in mind that the Chongqing's health examination costs just about the same for 6 months as elsewhere for one year.
Cheers and beers to all