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I think this is the key. You are selecting which pairs breed. Your selection will probably not match what the owner of the original line would have done. They are not that line anymore.
I think it is important to start with good stock, and I don't see anything wrong with mentioning where the parent stock came from. After all, somebody might be looking for fresh genetics to mix with their birds which may have come from the same line. But after you have selected which paretns go together, they are no longer the original line. Their background has a specific line in it, but there is a distinct difference.
This is even more personal opinion. I don't think you should call it your "line" until you have gone through a few generations with your culling practices and develop a consistency in your results. By this, I do not mean every bird is of equal high quality. I mean that you consistently get some birds that are of high quality.