I think I have asked for this feature in the past also, but I am happy to weigh in here also.
Our problem is also with our automated tests that are not run by a “person” but under the automation account. When the triage teams root cause the failure and create a bug, they currently have to log into a second window under the automation account to add the bug information associated with that run. We also do not like to add another run as it only messes up our run information and we still would have failed runs that do not have bugs associated with them.
One approach that could work for us is an API that allows us to add the bug information. This is functionality available through the GUI that is not available through the API.