Hmmm, I agree and disagree with you.
I doubt Rothboard would describe his viewpoint as being simply that "property is a god-given right while water isn't," even if you exclude the god-given part. It's more that property is an institution that develops from organic human action and self-organization. And in his vision people end up self-organizing into groups that will defend some version of property rights using threat of violence if necessary, and he goes further and thinks that, due to the nature of the market of violence, most will converge onto roughly similar versions of property that are best suited for human living.
My take on that is that this has already happened, but as it turns out the market of violence lends itself to aggregation and monopoly. We call this monopoly supplier of violence the State, which has found it utility maximizing to form a set of contracts, implicit and explicit, with most of the different parts of society, including price discrimination, loss leaders, etc.
In other words, Rothbard left out public choice and the economics of the firm, and when you add those into anarcho-capitalism you get... social democracy.
I deeply admire, though, his capability to imagine a different, more decentralized, and free-er world. Like most visionaries, his greatest flaw and strength is his utopianism.