It all hinges on the definition of "urbanized area." LA is indeed a denser place than it is generally given credit for and, as the op-ed claims, its basic geography was formed by streetcars and not the automobile. But "urbanized area" is a particular construct which, given LA's geography - water on one side, mountains/desert on the other - is going to provide a measure of its density ranking which wouldn't apply if others were used.
In measuring the density of a city one has to choose the boundaries. Are we talking about the political city of Los Angeles, even though the conceptual/economic city certainly doesn't really stop at its artificial borders (is Santa Monica really somehow distinct from LA? Politically yes, but conceptually no). There a variety of measures of "city" which are all some combination of what we'd like to measure and what we have decent consistent and easily/regularly gatherable data for. In one sense "urbanized area" is the best definition - as it basically starts with the urban core and then adds on all the contiguous dense bits.
The Census Bureau delineates urbanized areas (UA's) to provide a better separation of urban and rural territory, population, and housing in the vicinity of large places. A UA comprises one or more places ("central place") and the adjacent densely settled surrounding territory ("urban fringe") that together have a minimum of 50,000 persons. The urban fringe generally consists of contiguous territory having a density of least 1,000 persons per square mile. The urban fringe also includes outlying territory of such density if it was connected to the core of the contiguous area by road and is within 1 1/2 road miles of that core, or within 5 road miles of the core but separated by water or other undevelopable territory. Other territory with a population density of fewer than 1,000 people per square mile is included in the urban fringe if it eliminates an enclave or closes an indentation in the boundary of the urbanized area. The population density is determined by (1) outside of a place, one or more contiguous census blocks with a population density of at least 1,000 persons per square mile or (2) inclusion of a place containing census blocks that have at least 50 percent of the population of the place and a density of at least 1,000 persons per square mile.
All of Los Angeles and the connecting bits are quite dense. Until, sudddenly, the LA urbanized area basically stops (at least until the developers get there at which point another dense development is added on). It isn't completely uniform in density, but much more than the UAs of older east coast cities. In older cities density declines more sharply as you move away from the center and instead of going from "dense areas" to "nothing" rather quickly the urbanized area definition includes a lot of "not so dense" bits which bring down the average.
Density rankings based on the actual city municipality or county-based measures put Los Angeles much lower in ranking.
The reason why LA is dense but doesn't feel dense is that while its basic geography was created by streetcars, the urban highway system was subsequently grafted onto it. So, while it's pretty dense overall it lacks easily identifiable super-dense cores which create walkable areas. Everything is spread out just a little bit too much. Best of both worlds, or worst, depending on your point of view.
So, LA is both very dense AND very sprawled.