Well, sounds like that's why it thinks there is not enough space. Have you checked to see what you have on the phone that might be taking up that much space?
I did, and I can't figure out why this one would be more than double all my previous ones.
Tried to do a backup, it said it would take 3 hours, no worries... then I got an error message that it failed. Tried again, and again. 3x it failed after about 2 hours. 
That mail you mention is what's in your mailboxes on iCloud. Including anything in saved, trash, junk, sent and inbox folders. That's not a backup. That's just what is currently being used.
I had 2 phantom backups eating about 200MB. I tried everything short of a restore because of my watch, so I gave Apple a call. First representative tried to tell me that the iPhone needs 200MB of iCloud space even if you don't have backup enabled. I immediately asked for someone else, was not going to waste my time with that nonsense. The second rep was able to delete 2 phantom iPad backups and got my entire 5GB available for usage again.
Unsure. But the rep gave me his contact information and he said if it does it again, send him an email or call him and he will remove it and then forward it up to engineers. They must be somewhat aware of the issue if they are able to remove them. But I did two backups last night (iPad and iPhone) and my space is being accounted correctly. So it's a good sign!