Practically, it means that if you come by a Z visa you have to do the paperwork first like getting your residence permit and your Foreign Expert Cert....

You can't get your residence permit and your FEC. Your employer dose that, FEC first, and then RP, by the way!

Most public schools follow the legal procedure anyway in this respect, there are only some bosses of crappy private training centres who do this kind of illegal thing, I guess.

You guess wrong! It's common practice for Chinese employers to take their time getting a new FT his (or her) RP. In the meantime, they can ask your students if they like your teaching. If not, you can be let go without an employer having wasted his time and money obtaining an RP for you.
Besides, FAO's usually wait until all of the FT's have arrived at the start of a new semester before going to the PSB to get the RP's - they can save time by only paying a single visit to the local PSB office to obtain RP's for all of the FT's!