The short answer is: NO! While it is true that 15 grams of light roasted coffee contains less caffeine than its darker counterpart, increase in caffeine content during the roast is not the one that cause it.
Each individual coffee beans contain certain amount of caffeine and is pretty stable during roast. However, coffee beans shed its water contents, making them lighter as they progress through the roasting phase. This makes a single dark-roasted coffee bean lighter than its light-roasted counterpart. Because darker coffee beans weigh less individually, there will be more coffee beans in a cup of 15 grams dark-roasted coffee than 15 grams of the lighter ones. And because there are more coffee beans, naturally, there will be more caffeine content in 15 grams of dark-roasted coffee compared to the light-roasted one.
In conclusion, the reason why a cup of darker roast coffee contains more caffeine is just because there are more coffee bean being brewed and have nothing to do with the increase in caffeine content during roast.
So, it’s a myth.