Quite the opposite: It should, in an ideal world, be perfectly safe to share your credit card number with everyone, because all it should be is arguably an account number.
Payment initiation or confirmation can be an entirely separate layer (such as chip + PIN or 3D Secure).
This is actually the goal of European regulators right now (with some carve-outs for low value and low-risk transactions).
At the moment you need to provide a complete "private key" to each processor, who up the ante to: CC Number + Expiry + Security Code + Name + Address. They all ask for it, so any of them could leak it, or it could be phished.
Payment initiation or confirmation can be an entirely separate layer (such as chip + PIN or 3D Secure).
This is actually the goal of European regulators right now (with some carve-outs for low value and low-risk transactions).