I believe the issue tracker should be separate (API wise) but hooked in. Manipulating it outside the codebase is what people want. That doesn't mean it can't also be a distributed system, just that it should be separate from the code.

(Reducio ad absurdam: if you want the bug tracker integrated with the code, keep the bugs as text files in a subdirectory of the git repo: you can then file bugs by pull request, and update the state of the bug along with commits to the code)