I can't disagree with that. I'll just point out that we've repeatedly set up timed stages to test just that question. Admittedly these are IDPA/USPSA shooters mostly, but also 2- and 3-gun shooters, and none of us are strangers to carbines (or shotguns).
What the exact reasons are that the sharp-end guys you've worked with choose to fight with a carbine over a handgun, even at short range, I'm sure I can only theorize about -- but I'd imagine that the facts that they put vastly more rounds through their M4s than their handguns, and that an across-the-room fight often will seamlessly flow into a down-the-street fight or an across-the-field fight probably have just as much to do with that as whether or not they would be (or could be) faster on close-in work with an M9.
EDIT: And, of course, if I'm going to be fighting 95% of the time with a carbine, I'm not going to sling it and transition to a handguns every time I enter a doorway. The differences in speed aren't nearly worth the time and hassle, and bother of a swinging slung carbine hanging between your knees. If you're going to be carrying the rifle in a combat zone, carrying on fighting with that gun under all circumstances only makes sense. Heck, if nothing else, a soldier carries at least 240 rounds of 5.56 right? As compared to maybe 30-45 rounds of 9mm FMJ? Lots of pluses for sticking with the carbine if that's your fighting gun.
It would be interesting to do some actual research into this. Figuring out how to control for experience/training differences, how to define or test a radius of effective dominance rifle-vs-handgun, etc.