Well, yeah, but...
Time of death is way fairer because the relative levels of fame of any two deceased have a lot of impact on how quickly a death notification can be posted
Re these two, nothing more specific than "Tuesday" offering itself for either atm, and loads of evidence their deaths have been widely reported but all reports appear to have come from a single source (likely one main news agency). Nacho's various death stories read very much alike regardless of where they're showing up.
A suggestion - if I can't sort this in a couple of days I'll donate to the obesity charity on behalf of both winners!