Is Romney Barring A Muslim From His Cabinet?

Here's the alleged quote:

I asked Mr. Romney whether he would consider including qualified Americans of the Islamic faith in his cabinet as advisers on national security matters, given his position that "jihadism" is the principal foreign policy threat facing America today. He answered, "…based on the numbers of American Muslims [as a percentage] in our population, I cannot see that a cabinet position would be justified. But of course, I would imagine that Muslims could serve at lower levels of my administration."

It would be a Hewitt-level feat of double-standards if Romney were to use someone's religious faith as a criterion for inclusion in his administration, don't you think? Powerline harrumphs. Geraghty hedges.