If we should set aside my second and third lines of argument, this seems to leave two possibilities. The first is that the libertarian case for free markets and limited government rests on some other conception of liberty, which I did not consider. Wilkinson does not suggest such an alternative. The other possibility is that the “liberty” in “libertarianism” refers simply to the institutions that libertarians favor—free markets and limited government—which are justified on grounds other than the value of liberty (simply grounds of efficiency, as DeLong suggests, or broader grounds, as perhaps in the works Wilkinson cites in the footnote at the end of his comment.) If so, then although the conclusion I arrived at is still correct, my initial characterization of libertarianism—as founding a political program on an independent idea of liberty—is mistaken.
What makes a liberal system of institutions distinctively liberal? Here are two options. A system counts as liberal just in case (a) it accords a certain priority to the protection and promotion of liberty, whatever its justificatory basis of this priority, or only if (b) the system accords a certain priority to the protection and promotion of liberty on the basis of the value of liberty alone.
If it's (a), then it must be possible to establish the priority of liberty on grounds other than just the value of liberty, or on "broader grounds" that perhaps includes the value of liberty among other values. If this is true of liberalism generally, it's going to be true of any specification of liberalism, including those that recommend a political program of "limited government and free markets." But then its no knock against libertarian versions of liberalism to note that, like all kinds of liberalism, the priority of liberty in libertarian theories is established by the appeal to a plurality of values.
If it's (b), then I guess I can't really think of any examples of a theory that derives the priority of liberty directly from the sole value of liberty. I can think of plenty of liberal and libertarian theories that derive the priority of liberty from certain deontic constraints that are supposed to get their normative teeth from the nature of nature or the nature of reason. There are two main kinds of bad liberal and libertarian theories, in my opinion: this kind and the utilitarian kind. According to neither does an independent idea of liberty play the key justificatory role. Yet it seems to me Scanlon thinks most libertarians see themselves as deriving their political program straight from the value of liberty and that if he can show that libertarians don't actually do this, he's somehow struck a blow against the libertarian's self-conception. I can't see the force of this.
I didn't gesture toward the "neo-classical liberalism" of Jerry Gaus and John Tomasi to suggest that even if there is no way to justify a program of free markets and limited government in terms of "an independent idea of liberty," there may yet be some justification "on broader grounds." I pointed to Gaus and Tomasi to suggest that however Scanlon thinks liberal institutions are justified, a program of free markets and limited government will be part of the general liberal program if the liberties accorded special protection in liberal regimes include robust economic liberties. The neo-classical liberal argument is that there is no principled basis for according special protection to political and civil liberties, while leaving unprotected various economic liberties.
The most interesting development in recent libertarian-ish political theorizing is the increasingly common abandonment of external natural rights or utilitarian criticisms of Rawls-style contractualist liberalism for a defense of the priority of economic liberties on contractualist grounds. I wish I had reserved more space in my short reply to make this argument more explicitly, because this is where the action is.