I'm tired,,,,, so,, hard to provide an answer.  Chiner is the Land of Go along 'n Get along.  The day u start driving yourself crazy about looking for Western definitions/explanations for things will be/should be the day you should consider 'hit the road Jack,,,,'.

Around here you get a visa if the outfit that sponsors you has the 'Pull'.  That's all there is to it.  Unless some weird circumstance where an outfit with more 'pull' is set on blocking you.

  国家外国专家局关于印发外国人来华工作许可服务指南（暂行）的通知

This is my question too

You can't have searched very well...obviously an admin post!

first result on bing for "China work permit" is this. 

http://www.visainchina.com/china_work_visa.htm

bullshit question. 

Their telling you to ask SAFEA. For a guy with a PhD. I can see that you lack the research skills.

For future reference, my friend in Shandong Province tells me that they no longer enforce the 5 year rule, but are strictly enforcing the age 60 rule now which will probably cause them a lot of trouble getting teachers. This is for the Jinan PSB, not sure about Qingdao, they are more strict but let old Mormons in their seventies teach at their universities all over the city, another exception that makes no sense.