Ash and Brock were the ones present during the first peril she got herself into as a beginning Trainer, and I think that alone creates some special connection between the three of them. Just like Misty only bothered to change her opinion about that bike-stealing brat Ash because she knew the kind of trouble he went through then.
As for the group dynamic, I really don't see anything wrong with it. The very first trio might have had the best chemistry, but I think they just had an advantage with the fact that the characters themselves were all new and the writers were playing around with them to present them as likeable people.
For instance, I think the AG group (especially in Battle Frontier) was the most "botched", if you can even call it that. It started out great, much better than the original group, but in BF, everyone seemed to be doing his own thing.
May seemed incredibly detached from the others by the end of AG, Brock...well, I guess he might do the same thing now if he was asked again, but something that struck me was how in that Contest he entered, he instantly agreed to go with Yuma without hesitation, without thinking about his friends even once. He might be a love dork, but that shocked me nevertheless. Ash was the same as always, and Max really seemed to be the only one who really wished to keep them all together.
Ash/Dawn/Brock don't even come close to showing that sort of indifference toward each other.
