How can someone be approved for a medical waiver, sworn in at MEPS, picked their job, then told MEPS did not approve the waiver?

There's no one above the MEPS, they are the gateway into all the branches. They don't set the standards of enlistment, only enforce the DOD and various branch policies and applicable laws. Basically, it's a screening station.
I've never heard of someone being sworn in without waivers being approved. That would mean that this person signed a contract, is in possession of a DD 4/1 and 4/2 and entered into the delayed entry program.
The only thing I can think of is if they weren't qualified for the MOS they requested and didn't receive approval for an exception to policy.