That every request made through the edge browser for a non local user is associated to his/her live ID is pure coincidence ;)
Sometimes when I look into my dns logs, I cry a little bit inside too.
but firefox has different dns requests going to their servers as well.
A few of them actually do make sense for a normal user (i.e. the Wifi portal stuff). But you can disable it if you spend some effort on it or you can also use an alternative build of Firefox without it. Not great, but also not terrible imo. Sorry, that I have no English source.