Yes, you can pay using your own link, except don't do that too much, as your CC will get banned by ClickBank.
That's absolute nonsense! Your CC will not get banned by Clickbank at all. It even specifies expressly in Clickbank's terms of service that you are allowed to do this. Why do people (a) believe such stupid things and (b) try to convince others that they're true? How else are you supposed to get hold of a copy of a product you might want to be an affiliate for, if the vendor doesn't give review copies ... buy it through someone else's affiliate-link?!?!
You can only buy through your own link 3 times. On the fourth buy you will be severely violated. You know, sexually. With a hammer. Have a nice day.