Thought-provoking. I find a lot of this hard to believe, but I have no evidence. (Does no one live in Isle Royale National Park? It has permanent park rangers, surely. Don't they count? Where do they give as their permanent address if they aren't allowed to list Isle Royale?)
I was most intrigued by the relatively large swaths of empty land in Pennsylvania. I've never drive through a part of PA that I couldn't imagine at least some people live relatively close. I guess that is the problem though... I was on a road.
This map is correct, but you have to keep some things in mind. Firstly these are based on blocks. If a park ranger lives in one, then that block is taken, but only that one. Secondly, keep in mind a lot of this will be developed, but no one is living there, such as in highly industrial neighborhoods. Third, of course in less urbanized areas, blocks are going to be much larger due to the way blocks are determined by the US, which is a surprisingly complex system of measurement.