Tino: GREAT post. I will respond to it in depth later.
I bet the answer to the Harry met Sally question is this:
It depends on the people involved.
Of course, this answer is no fun, but let's think of it this way:
Make two lists, one for the qualities you want in a best friend, the other for qualities you want in your ideal romantic partner. Now, the degree of correlation between the two lists determines the probability of you thinking of a friend as a potential sex partner.
Back to the original question:
Can two singles of opposite sex be "friends" in the way that neither of them ever think of the other as a potential sex partner? The answer is yes if the friend list and partner list have no correlation. And the answer is yes if they are both in denial about wanting to fuck each other.
Of course people can choose not to act on feelings. But I don't think that is what this question is really about.