Ayn Rand's Naturalistic Fallacy

Reading about Ayn Rand's philosophy of 'Objectivism' in Brian Doherty's excellent history of libertarianism, Radicals for Capitalism,
I came across the following passage:

Her essay collection The Virtue of Selfishness - the title chosen because she knew it would offend people - begins with an explication of Objectivist ethics that try to solve, in a bold stroke, the ancient moral philosophical problem of how to derive an "ought" statement from an "is" statement - how to make the facts of reality lead to an undeniable moral conclusion. "The fact that a living entity is, determines what it ought to do." A human being [which is a mammal surrounded by competing mammals] must think and reason to survive, otherwise we are not well equiped to outcompete our mammalian competitors for food. We are not faster than the gazelle or stronger than the lion, yet by using our reason and intelligence, we can surpass them in the struggle for survival...

This conclusion, upon which she based her Social Darwinian/Nitzchean ethical system, is supposed to resolve the 'naturalistic fallacy', which states that a fact (something that "is") and a value (something that "ought" to or "must" be) are wholly distinct things and that one cannot logically derive the latter from the former.

But surely there is a glaring logical fallacy here. For her analysis to be valid, an ethical value - either a moral prescriptive ("ought") or a moral imperative ("must") - has to be derived from the fact of our biological existence. But her use of "must" in this context is not as a moral imperative, it is merely used to make a conditional statement of fact, i.e. "we must act in this way if that outcome is to be achieved, and if we don't act in that manner, then it won't be achieved".

So she has simply moved from the fact of our existence to the additional fact that our continued existence depends upon certain contingencies (from "is" to "is, so long as..."); what she has absolutely not done is move, in a logically valid way from "is" to "ought".