Just an idea..... you know how in Ootp Sirius was distantly related to people like Malfoy and some Death Eaters? Well, in some way Harry could be related to Dumbledore but just distantly. However, he wouldn't be able to 'take him in" because the relation is not as potent as his aunts. You follow? Like, if Dumbledore was his great uncle twice removed or something, his relation would be so watered down the blood charm would never work. Or, I could be wrong......
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... anyway, it's all speculation.