1) The same bug in both places, with different buy useful discussions in each. How do you merge these two bugs? How do you mark one as a duplicate?
2) The developers of the program (or web-site) probably don't know you exist, so while there might be a great discussion related to the bug, the person who can actually resolve it doesn't know.
3) Assuming you're not the only "foreign" bug-tracking system for a program (or web-site), how do you interact with the other "foreign" systems?
4) There's no barrier to entry, so there's no incentive to creating anonymous bugs or to using the platform to rant at the developer.
You're not alone with these problems - GetSatisfaction and UserVoice have the same issues. My suggestion would be to create such an amazing bug-tracking system that the developers WANT to use it as their primary source. Then get bought by Github.