Let's look at the github model -- there's no
assignment at all. I just
file a bug, maybe make some comments on it to say I'm working on it, and
some time later I submit a pull request referencing the bug and saying, "I
fixed it". That seems to work fine for collaboration, and offers no
GitHub issues are owned by whoever submitted them (and the project
owner). You can't for example convert an issue to a pull request
if you are a third-party.
But you can always reference an issue in a commit or a comment though.