I actually think its the complete opposite. eg, Facebook, Linkedin
https://www.facebook.com/notes/facebook-engineering/under-th...
http://venturebeat.com/2013/04/17/linkedin-mobile-web-breaku...
They tried web-based apps. They said the experience isn't what people expect as with native.
This is exactly why Firefox OS exists. Because the web had become stagnant on mobile due to a lack of competition.
Do you think that every vendor purposely downgrades the mobile experience(even vendors like samsung which don't have a reason to favor native vs. web apps)? It doesn't make sense to blame mobile safari, chrome, and ie mobile when google, apple and Microsoft put a lot of resources into their development.
They put far fewer resources into the web on their devices than they do the native sdk. For example, last year Google created "Project Butter" because people were complaining about touch performance on Android. There is no Project Butter for Chrome on Android, even though it has touch responsiveness issues too. Why? Because the former costs them sales of phones and the latter does not.
This is why Firefox OS is important. They are putting all of their resources into making the mobile web better which, hopefully, will lead to a better mobile web on other platforms as well.
Your second is demonstrably false - both the Mozilla Foundation and its wholly-owned Corporation have awesome boards of directors, and from my experience (having worked and volunteered for Mozilla for many years) the leadership is extraordinarily sensitive to outside advice and criticism from people outside the organization as well as inside.
Mobile has incredibly high barriers to entry, and breaking into it is not easy nor simple, and is not going to happen overnight. However, moving mobile away from locked-in native platforms and onto open standards is a laudable goal in my opinion, as is making inexpensive, capable devices for the next billion people who are coming online.