Hello this is the first time I am using the jquery bug system.
It might be a good idea to fix this. Not just in the live region which is for readers but also the tooltip content both cause this issue with radio buttons.
To fix this I created a Pull Request modifying the _open function to strip name and id from both which required first passing the accepted content type into DOM objects. here is the PR - https://github.com/jiabaowu/jquery-ui/pull/1
Incase it is decided that this stripping of name and id from tooltips is merged I also created a pull request for the unit tests associated with this new feature. PR - https://github.com/jiabaowu/jquery-ui/pull/2
Thanks a lot if you take a look at the PRs, I think its good to try to make tooltip as isolated as possible from the rest of the DOM.