From the screen shot you are using gmail app correct? Is your gmail account enabled as an IMAP mail account? If so, have your tried setting it up in the iOS mail app and reading mail there - do these phantom emails pop up then?
My thinking is this may be some issue with the gmail app itself, since from your last post it would not appear to be a server or account problem on Google's side of things. If the gmail app is using some sort of database (sql lite or something like that) for it's underlying mail data structure, it may be a glitch in the app itself.
For what it is worth, I only use the iOS built in email reader, but I do have 3 IMAP enabled gmail accounts on my iPhone - I've never seen anything like this in any of my gmail accounts (but a two of them are not heavily used either - really just have them for the google voice numbers I wanted).