What about those FT's who don't have degrees, or relevant ones, aren't they employed "somehow"?

Not like they used to be.
It used to be pretty easy to talk one's way to a Residence Permit without a college degree.
No more. In most places the Labor Bureau won't issue a Work Permit for teaching without a degree...and without a Work Permit, you can't get a Residence Permit. Without a Residence Permit, you're an illegal foreign worker in China.

This has meant that a lot of people without degrees no longer have the option of legally teaching in China. I hate the pain this has caused people, but it's now the law...and for once, the Chinese authorities seem to be actually enforcing a low. I certainly won't argue that people without degrees can't be good teachers- I've seen it happen many times- but on the other hand requiring teachers to have a college degree doesn't really seem like an unreasonable thing to ask.

About the only schools hiring teachers without degrees are those who don't have licenses to hire foreign workers...in most places you have to be in business for a year before you can get such a license. These schools tend to be really desperate, because without foreign teachers they can't attract as many students or charge a premium tuition fee. Sadly, such schools are most definitely above telling would-be teachers that it's fine to work for them without a Residence Permit. Even sadder, quite a number of expats fall for this lie.

It's NOT fine to work in China, for a Chinese company, without a Residence Permit...no matter what anyone may tell you. Yeah, some people get away with it, but increasing numbers of people do not. All it takes is one cop in a bad mood to bring everything crashing down on you. Working without a Residence Permit is a CRIME in China. So is working for an unlicensed school, whether you know about that or not. Doing these things exposes you to the general litany of punishment China can mete out to foreigners: heavy fines, possible detention, probable deportation, and forcible sodomy.
Well, OK, maybe not that last one. But you may end up feeling like it happened...

So yeah...working illegally in China is not a smart thing to do. Be legal, or be gone!