I think it's the responsibility of the provincial education bureaus to verify academic qualifications, and then issue an FEC to degreed foreigners. Without an FEC, it's impossible to obtain a work visa.
I know some PEB's either take backhanders from Chinese school/college directors or simply do not check up whether the degree certificates are legit. The latter is hard to do, as western unis won't assist them in that process, so I'm led to believe. It could also be that in some underdeveloped provinces that have difficulty attracting foreign teachers, the PEB's compromise the regulations in order to accommodate the schools. I'm not sure how strictly said regulations are meant to be applied, and the other thing is there's often no rule of law in China.
In Taiyuan, I know for a fact an Aussie with a two-year college diploma and a separate one-year one got an FEC after the school's director wined and dined the local PEB. He'd been teaching on an L visa for two months, and then did the HK run. I also know there's a guy without a degree teaching in a Shanxi backwater at a normal primary teachers college. He's been there for five years. It's said he's well in with one of the PEB. Another lax province in this respect is Jilin, but Sichuan is strict, as is Shandong now - that one never used to be. Inner Mongolia Autonomous region gave an FEC to an old alcoholic ex farmer some years ago. He only had a certificate for attending a night class course for six months! They even accepted a letter from his solicitor in the UK stating that he was a person of good character instead of insisting on the enhanced disclosure police check from the UK police! That's an extra hoop for foreigners who want to teach there to jump through!
So, it seems some officials aren't doing a good job. Anyways, it doesn't affect me as I have a real university degree.