For myself, I consider the birds I get from an original breeder still 'their' line until I introduce new blood. While I consider all birds 'mine', I still will give credit to the original lines they come from, but not to the extent that I am taking credit for someone elses hard work.
I consider the bloodline 'mine' as soon as my first generation has had babies. Those babies are now 'my' personal, original bloodline. I dont mind telling folks where I got my original stock, since I think people want to know the history of some of their birds, and it helps to be able to say I started with quailty stock from a known and respected breeder. Its pretty hard to come up with your own bloodlines without using someone elses', and where better to start than with a line that is well-known and respected?
Really, unless you started with an original, heritage breed that has had zero other bloodlines introduced and its been in your family for generations, we all start out with someone elses' bloodlines. Its up to us to create our own from there and call them ours.