Your overall claim that dark roast coffee doesn't have more caffeine than a lighter roast of coffee, is correct. But it's important to keep in mind that the difference in caffeine between light and dark-roasted coffee is so small it's insignificant and unnoticeable. Most of your explanation is correct. Caffeine content does actually depend on the time frame that the beans are roasted. However, it is important to mention that dark-roasted coffee does actually have more caffeine by weight volume. Here's a quote from an article explaining the math:
"Here’s how the math breaks down: Take 1000g of green coffee: it has about 12g of caffeine, or 1.2% of its total weight. Roast that coffee to a light roast, and the finished weight is around 850g. But there’s still roughly 12g of caffeine molecules in that roast, making the caffeine percentage 1.4% now. And if the coffee is roasted to a medium roast, the finished weight might be 800g, with still roughly 12g of caffeine inside, giving a caffeine volume of 1.5% of the total weight. Take a bean like a maragogype and roast it full dark, and the resulting 700g of coffee – which still has roughly 12g of caffeine inside – has 1.7% of its volume as caffeine.If we use 35g of roasted beans to brew 500ml of coffee, here’s how much caffeine, by weight, is stored in those 35g samples (noting that not all this caffeine will actually make it into your brewed cup of coffee):
Light Roast: .49g (490mg) of caffeine
Medium Roast: .52g (520mg) of caffeine
French Dark Roast: .6g (600mg) of caffeine"
Source: https://coffeegeek.com/blog/techniques/a-bit-about-caffeine/
The general consensus is that caffeine content in light and dark roasts depends on how you measure and brew your coffee not necessarily just the moisture levels. The difference in caffeine is negligible as long as the coffee beans are measured out by weight and not the volume of brewed coffee.
Here are my other sources that back up this statement:
https://pmc.ncbi.nlm.nih.gov/articles/PMC8228209/
https://blackcreekcoffee.com/blogs/coffee-talk/which-coffee-has-more-caffeine-dark-or-light-roast
https://www.healthline.com/nutrition/light-vs-dark-roast-coffee#caffeine-contents
https://valor.coffee/blog/does-light-roast-coffee-really-have-more-caffeine-than-dark-roast