See I think that's a red herring. Textual proof of my thoughts would be long, since it's just a general trend, not anything specific. I can see the Slytherin connection as being an inspiration, but I don't see it as conclusive that it was in his nature. There's a lot of stuff in his upbringing that point to a nurture viewpoint of why he is. There's also the whole Harry-Riddle connection that would be meaningless if bloodline is the only factor.
In fact, bloodlines have been shown to be given too much weight in the wizarding world, which is why you have mud bloods and squibbs. They trace their lineage like it means something, when it really doesn't. But, like I said, my arguments are a little too nuanced for me to feel like writing right now (especially since I haven't read HBP in quite a long time).