It seems to me to be a cop-out to suggest you can't have good public transport in a low density area. I come from the city of Perth in Australia which is very sparse and it has managed to create a very good intermodal system with light-rail corridors connected by an extensive bus system that feeds to the rail system. You can get pretty much from anywhere in the city to anywhere else with a bus service within half-a-mile, often involving trips of 50 miles or more.

While Google Maps' colors don't make it easy to visualize, perhaps you can get a sense of it: https://maps.google.com/maps?q=Perth,+Australia&hl=en...