I could be wrong. My information is a few years old, but people do drive across Saudi from the UAE so I assume it can be done from other bordering countries. Maybe try calling the Saudi embassy in Qatar?
It also happens that beauracrats to say something can't be done because then you go away and don't bother them anymore.
Thats a really interesting information, because eventually I may be interested in taking my car with me from UAE, in that case driving through Saudi comes into play.