This statement is true to a fairly great extent.  The auto industry was definitely responsible for much of the boom.  However, there were also other factors that were important.

Cars were important in a number of ways.  First, of course, they were important to all of the people who worked in the auto making industry.  These included people who actually put together the cars, but it also included those who mined the iron ore, smelted the steel, made the tires and glass, and many others.  Cars were also important to people in a number of industries that rose up alongside of cars.  Cars were important for people who got work building roads, for people in the oil industry, for people who opened service stations, and for people who ran motels.  They were also important because they opened up new areas for residential neighborhoods.  There was not a huge boom in suburbanization as there was after WWII, but house construction did help the economy grow.  In these ways, cars were a major driver of the economy.

However, there were other things going on.  There were also many kinds of consumer goods that were coming to be available.  These goods were affordable to many people because of innovations such as buying on credit.  People wanted the goods in part because this was the time when advertising really started up as a major industry.  What this means is that cars were not the only thing behind the boom.  They were very important, but so were other kinds of goods and services.