Yeah, true, so basically SNAFU. I would not expect any legislation about illegal employees in China to be directed against the native population. That would be contrary to norm.
Well, to be fair, the legislation targets both equally. Schools can be, and have been, heavily fined for employing people illegally. The laws that are actually on the books do not say "foreigners get fined and deported, schools get told they have been very very naughty." The schools are supposed to be punished.
While hong bao work in many situations, in larger places the chances of a rogue school being able to get out of paying a fine are a lot slimmer. For instance, there are thousands upon thousands of illegal mom and pop schools in Beijing and most of them wouldn't even know where to start with the bribes. You can't just show up at the police station with a hong bao, it doesn't work that way, you have to have an in, especially if you're a relative nobody -- and lots of small school owners are (I should know, I used to be one. We tried to cultivate guanxi with a local PSB guy and while he was able to help out a bit with some visa stuff for a few of our teachers, but would have been pretty useless in a real shit has hit the fan situation). And even when you can call in a favor, sometimes the connections of the person doing the reporting trump the connections of the school. And, theoretically, a well connected foreigner could also get a slap on the wrist and nothing more if he called in favors with the right people. The system isn't set up specifically to punish foreigners and let locals go scot free, locals are just more adept at abusing the system.
It is true that your New Orientals and your EFs are probably not going to have to worry. But schools with decent enough connections and enough financial solvency generally can also get permission to hire foreigners legally. It actually is not really all that difficult. Your school can't get it if they are brand new though, and lots of little startup schools never make it past the required 2 years.
It is a risk for foreigners to work illegally but that doesn't mean that schools take no risk whatsoever. The reason both sides do it is because by and large, people tend not to get caught.
Finally, I don't know why I felt the need to expend so many words defending the Chinese government, they certainly don't deserve my sympathy, but I felt the law was being slightly misrepresented here. Or maybe I'm just in a contentious mood.