wow - that's encouraging. I would have thought the camera would keep swinging round to the side or the front as you moved about on the bike.
Unfortunately, it might, depending on what bike you ride.
If its got an upright, more of a 'shopper' type geometry, you might be ok. The more bent over and aggressive you are, the more likely the camera WILL swing round from your back.
I sometimes carry a camera in a rear rack, but if I do, I don't take one which I know has a sensitive image stabilization system (as they are prone to damage from bumps), or one with a long lens (as you can deform the camera mount). Plus I always make sure its in some kind of VERY padded bag ... maybe even with a an extra piece of clothing placed underneath to further absorb the knocks and jars you will inevitably get.
If I'm on a MTB, then its a PITA, but I stick it in the padded bag and in a rucksack as the body tends to absorb the worst of the bumps. You tend to take less photos that way though :-(
Another option I used a lot when hiking somewhere, is to use Peak Design Capture clips mounted on the front straps of a camera backpack. They are excellent. This might work with a bike type setup, but I've been too lazy to transfer the mounts over as yet to try!