The jury’s still out; most of these explanations have a lot of “may” and “perhaps” and “could” in them, and they’re basically side observations of experiments that were looking for other things or were done in other species.
To really answer this for sure will take studies designed to actually test it; which so far as I know haven’t been done yet.
But, hyperbolic public news stories aside, I doubt it. Weight loss studies from the early 80’s often showed that switching from sugared to diet cola was one of the biggest changes you could make to increase weight loss. Recent studiesin humans (not rats) show similar results. And from a strictly medical standpoint, it’s hard to imagine that an insulin response, however strong, would result in the consumption of more calories than the 150 or so saved by not drinking sugared pop.
I no longer have access to the content, but there’s a PubMed review study of many weight gain studies here. Their general takaway (someone please confirm) is that the evidence is fairly strong that diet drinks decrease weight gain, as you’d expect.
The single most-quoted study is the most suspicious, in which while studying something else, it was noticed that the diet soda drinkers gained more weight. This is a classic reversal of cause and effect (aside from some who prefer the taste, most folks only drink diet pop if they have weight control issues), and probably doesn’t indicate anything: the controls were not designed to control for the result that the everyday media reported.