We use pull requests as a form of code review; each team member works in a fork and uses pull request to get their code reviewed and included in the master repository. They work on issues that are in the master repo's issue tracker. When a team member references or closes an issue in the commit and that commit is accepted in a pull request, the issue is then updated by the user accepting the pull request.
It would be better in my opinion to have the issue update either by the team member issuing the pull request if that account is a team member on the repo to which the pull request is sent. If this is not the case the issue can be updated as it is now, by the account that accepts the pull request.