The gravity issue, frankly, sounds like a load of hooey to me, unless you're planning to wait a long time before cutting the cord (like more than 30 minutes).
Granted, if the baby's on your chest with the cord attached and unclamped, then it ishigher than your placenta, so the blood has to be pumped a bit harder to go up, but the same argument could be made for never putting your feet higher than your heart. Of course you can do so--just don't do it for a long stretch of time, or your feet will fall asleep. Are my feet in danger because the blood and nutrients are somehow being lost by being higher than my heart?
I had my son on me, with the cord attached, nursing to help push out the placenta, in a hospital, for a good 15-30 minutes. The CNM clamped the cord after it stopped pulsating, then I cut it myself. Placental birth was a breeze. There was never a problem. As the CNM told me, waiting to clamp/cut the cord means that the baby's still attached--no one can whisk him away!
Methinks your OB is either misguided or has an agency as someone mentioned above...
Good luck and stick to your guns,