He's scored another job in another province - one where these new rules are not fully enforced - and been told to leave China. He will be issued with a brand new invitation letter so there's (apparently) no need for a release letter from the place he's walked out of.

I was under the impression every province now required criminal check and degree verification?

I can't see how the Hong Kong visa run is doable anymore....perhaps it depends on the psb of the province of China issuing the invite letter?