As for the question: "I think the most interesting question here, though, is:
Is love (or any feeling for/about a person) stronger/somehow more valid if it is based on the person alone, rather than on the person in the context of the relationship?"

I'll say that I think that its more valid in the context of a relationship. Loving someone is ok, but loving being a part of a particular "us" is much better. On the other hand, I think there's a lot of societal pressure that you should like the person just based on them alone, which has somehow become the romantic ideal. I think this ideal does more harm than good though.

And Alec is right, unrequited love is really ultimately less based "on the person alone" then real love is.