I don't know if Adobe doesn't understand "the web"; I think what happened here was just the landscape shifting out from under Adobe. The iPhone wasn't going to support Flash, initially because the power economics didn't work. Once the App Store was released, there was no way Apple would allow out-of-band application development technologies.
So what happened is that, to reach this new segment of the market, web developers needed to develop two versions of their applications -- one for iOS and one for everybody else. This in turn spurred development of non-native web technologies, for those applications where a fully native version wasn't feasible, which further reduced the demand for Flash. Adobe was forced to try and play catch up, and that's a really tough position to be in.
Good riddance, but I'm fully expecting Flash's niche as a provider of abusive advertisement and wretched restaurant menus to be filled soon enough. To paraphrase Jurassic Park, "shitty software will find a way."