Bull. This is a myth perpetuated by those who cling to their cars, and the ignorant. Rail service was prevalent in this country up until post-World War 2, and from what I can tell, the country didn't get any larger after WWII. Detroit was designed around the automobile and is now RAZING over 20 square miles of abandoned cityscape, thereby shrinking. The city leaders are now reviewing plans for a smarter and better laid out city. City planning in the US has been very poor for the last 60+ years, and hopefully we are now realizing what a folly the automobile truly has been for us -- and this is coming from someone who has been a complete gearhead for most of his life.
City planning hasn't existed over the past 60+ years, and I would even go so far as to say that the formal schools of urban planning lost their clout around 1930-1940. And, yes, the automobile was a huge folly because it instituted this device that pollutes, is expensive, is unsustainable, and also has a vague, sociopolitical romance about itself that is still entrenched in Americana today.
The country didn't get any larger after WW2, but metropolitan areas' densities plummeted around this time because the average area of a metro area exploded whereas population and infrastructure (besides the Eisenhower Interstate Highway System) remained stagnant. This was because of the rise of suburbia in the 1950s, which also had a strong sociopolitical notion attached to it: "America" became owning a car, yard, and your own lot in the suburbs, and commuting to work. This is still romantic for many people. Lack of density renders public transit relatively useless even if it were to exist---LA is a good example of this. What an awful city in many senses, but particularly, the urban planning and transit notions of the place.
Around the same time, funding for newer and more updated public transit began stalling in the 1960s as white flight became evident, urban decay increased, prospective efficacy of transit fell because of falling density, and as a result, there was just no one who wanted to fund public transit. Property values in urban areas fell rapidly, making these areas a poor choice for investment and a bad move for politicians as they were becoming more and more populated by minorities and people who couldn't afford their own property in the suburbs. Combine this with the fact that public transit always runs at a loss 100% of the time, and that the federal government (who is in charge of most transit and the funding thereof) is innately biased against cities and in favor of rural areas, it becomes a very sticky political issue that generally no one is in favor of except urban liberals, even up to today.