That's assumes you are starting from no one having any to one person having them all. If someone had 1 billion in demand for bitcoins it would drive the price up, some would sell hoping to cash out, but others probably more would save seeing this big new interest as a sign of increasing value. You can't count out the sociology and the theater of it. Or other external forces like unstable/untrustworthy national currencies, or the value of relative anonymity.

I'm not saying there is, I'm saying there could be.

Say I owe money in those bills for instance :)