Arkadiusz, we’re looking at the same issue, and it seems indeed like it has something to do with the jquery on update.html. I can also report that it occurs in Chrome, as I experienced it earlier today.
The last patch you link to does somewhat the same thing, but at a different point in time. Commit 94bee… handles checking the boxes on submit, while the patch handles checking boxes during the ajax call(which is triggered by updates on the cc/bcc fields and ticket stats). However, the patch mentions cases where you type something and then click on a checkbox - our users have experienced this just by typing something then clicking on submit, so it should only be one call to updateScrips if I understand correctly.
I’m currently working on a fix. The obvious one seems to be to remove updateScrips from UpdateContent, but then a callback should be added to ensure that recipients are up to date. Another could be to remove updateScrips from UpdateContent as above, then add synchronous calling of updateScrips and checking of recipients.