It’s not really “hoops”, but laws – and the fault isn’t with the law or the process, but how it was explained to you….. quite frankly, they probably have a newbie or intern recruiter communicating with you who doesn’t know the process so fluently and they likely said you need X Y Z to get your visa processed, and in the end, the problem wasn’t with the legal change or what you provided – but with what was communicated to you that you NEED to provide. They probably said you need a health cert, you went to get one from what in your country is qualified to provide, but when submitting to the authorities here…was insufficient, and they are probably thinking “shit, we’re going to either lose a potential teacher (or whatever) or have to explain a reason why our process failed”….it’s a lose-lose, why? Communication problems. If you plan to come to China for your first time, no matter what school or organization you come with, you’ll experience a LOT of these….so if having to get a health cert from a different type of organization dissuedes you from coming over, I’d wager you’re likely a very, very short term candidate for living abroad and should consider going back to McDonalds or whatever 😀
No offense with the last sentence, point was, that’s a terribly small issue and you’ve got to toughen up if you want to live & travel abroad, which ultimately in my experience is WELL worth the effort of overcoming obstacles presented in minor processing issues.