You're not so bad off. The nut may be a LITTLE low, but it sounds like the builders carved the nut slots where they are supposed to be, and maybe the previous owner got a little carried away.
Fretless nut slots are cut lower than fretted because there aren't frets in the way. My personal preference when having a new nut built for a fretless is to have a business card worth of clearance - no more - between the E string and the fingerboard at the nut.
If you find that your open strings buzz a lot, you might have to have the nut raised a bit (business card stock works well for this; just cut into strips and keep adding them until you like the height) or have a new one built from a blank.
HTH!
