Fossil [1] repositories include a distributed bug tracker (and also a distributed wiki and a distributed time-based notes system), and provides a browser-based UI.
I've only read about it, not played with it, so don't know how close it comes to what you are envisioning.
It's a good idea! However, the distributed nature seems to make it sufficiently involved as to preclude a good UI (e.g., issues seem to use hashes), and the simple fact of not being git, regardless of whether it's better than git, is a serious problem for adoption. Bitbucket also learned this the hard way, and even made an April Fool's joke about it before realizing they had to primarily support git.
GitHub being centralized is a feature, not a bug. You don't have issues that exist in some people's repositories and not others. You don't have a question of who has the authoritative repository; either GitHub does, or GitHub doesn't and there's a note saying it's not authoritative. You can support things like have cross-site forks, but it's actively good for UX to have a single authoritative server for the current state of the project. (And you certainly don't want to require cross-site forks, since that would make it far more burdensome to submit a single patch.)
> and the simple fact of not being git, regardless of whether it's better than git, is a serious problem for adoption
I think I was a bit too terse. I didn't mean to suggest that someone who wanted to do everything (SCM, bug tracking) distributed use Fossil instead of git. The idea was to use git for the code, and Fossil for the bug tracking and wiki.
I've only read about it, not played with it, so don't know how close it comes to what you are envisioning.
[1] http://fossil-scm.org/xfer/doc/trunk/www/index.wiki