You do not need a formal bug tracking system in a healthy agile development team
Quite a sweeping statement. Let me explain.
The whole problem seems to come from a fundamental misunderstanding of what a 'bug' is. I define a software bug as "undesired or missing functionality". Now let's compare this to a definition of a 'story' - a story is a statement describing the desired functionality - i.e. it is an invitation to correct undesired or missing functionality... Sounds familiar!
In other words bugs are stories. And if they are really stories, then why treat them differently? Simply write them on cards1, throw them onto the backlog and let them be prioritised along with everything else. Bugs that are important to the Customer will always be done first. Unimportant bugs will get fixed eventually/never in the same way as unimportant stories would.
 I use red cards so that bugs are visible in the backlog. That way if they start to multiply the team can stop and fix the problem causing it.