No, not entirely true. Roughly speaking, 40MHz channel means each AP delivers twice the bandwidth/throughput as a 20MHz channel width. Of course, in the real world, it's not actually 2x, but it's close. That usually translates to needing half as many AP's, or being able to cover slightly more range. For example, if your goal is 10mbit/s everywhere, you might find that where a 20MHz AP delivers 10mbit, a 40MHz AP delivers 18mbit, so you expand your 10mbit coverage radius by some.
Of course, this all starts to break down if you are in an overlapping coverage radius situation, like a busy stadium / convention center where you really need 12 overlapping AP's or more to cover the same area. Then you might actually run out of 40MHz channels and find it advantageous to use 20MHz channels to increase density.
EDIT: Long story short, it doesn't change the coverage *range*, but it roughly doubles the data rate delivered at each distance. And most of the times when people say range, they really mean range at which the AP can still deliver some threshold data rate, like 5mbps or whatever.