I concede defeat on one aspect of the density thought experiment: the commenters convinced me that there are places that don't have "the density to support transit" even if everyone who wants to go anywhere takes the transit. Phelan, California and Fort McMurray, Alberta may be examples of this. However, there are three aspects of the story that I'm sticking to:
1. If these places can't support transit, most of them probably can't support roads either. That's "support" either in the sense of inducing enough tax revenue to pay for their construction and maintenance, or providing a public service that would be considered worth the investment.
2. Most of the places that are generally claimed to "not have the density to support transit" are of the kind that would have the density to support transit if it had a 100% mode share.
3. As Jonathan said, if you make driving expensive or unpleasant enough (or if you just don't bother to make it cheap and comfortable), people will move to places where they can access things easily through walking and transit. That's the transportation-land use cycle that I identified in 2008 (here seen in a cleaned-up version by Pantagraph Trolleypole).
So the next time you're tempted to say something about "the density to support transit," ask yourself these three questions:
1. Would transit work if it had a better mode share?
2. Does the area have the density to support roads either?
3. Would people live or work more densely if the car infrastructure was less subsidized?