Apple's support has really fallen over the years, from being the gold standard, to tin crap. The agent's typical mantra is to not get in deep into your system problems and were it not for community forums and search engines, these solutions would remain hidden from us. A prime example of this, is the company in Massachusetts (I believe), who had contested Apple in their claim that the recovered, water damaged phone could not retrieve the photos. They actually BANNED the owner from the communities for daring to contradict them - YES BANNED!
I was able to get my @mail "tamed" again by deleting all the mail apps from my iOS and OS/X devices and reinstalling the apps, then setting up the accounts again. Please bear in mind that if you are concerned about a Gmail account, they no longer push @mail in RT (Real Time). Once you reset your accounts on the apps, it will take some time for your accounts to populate with the folders and @mail objects..