According to the data that Davies looks at, the density of employment in our cities has a major influence on public transport use, more so than residential density.
Thus at the metropolitan scale, there seems to be a strong relationship between (weighted) density and mode share in US and Australian cities, at least for the journey to work. The density of both population and employment matter, the latter probably more so.
In a city like Melbourne where the dominant sentiment is pretty well to leave suburban residential densities alone, high employment density can have a real impact on mode share. Obviously that depends on adequate public transport being provided, but it also depends on the density and scale of job centres being high enough to create the congestion that makes cars less competitive.
A great post.