Actually I'm extremely surprised, given the my reading of "The Other YN622C User Guide" (very useful BTW - thanks.) As far as I can tell, I'm using a Class 1 flash with type B body, which should work fine.
The section on On-Top Flash didn't list any exclusions by type of class of flash or type of camera.
By the way the following do work On-Top Flash:
Type B with Class 2 flash: 20D + 622 + 550EX
Type B with Class 4 flash: 20D + 622 + YN560-II
Perhaps all Class 1 flashes do not work with all type B bodies, or more likely all Class 1 flashes do not work with the 20D. Or perhaps just one Class 1 flash (the 465) does not work with type B bodies.
Even a dumb flash should fire if attached to the 622 on camera.
Most likely Yongnuo did not test the 20D/465 combination with the 622. I wonder if the other 46x flashes have been tested. Perhaps someone from Yongnuo could answer that.
Are you setting the transmitter (not receiver) to mixed mode? That's what you need to do with the 20D. I have the 20D an 465 and don't recall the issue, but will check.