Towing Question - UHaul Auto Transport

I am a new owner of a 65 Sprite that I have to go pick-up.  I have been
told by U-haul that their the Sprite is too narrow to fit on their auto
transport (trailer).  I would prefer not to use a tow dolly.  Has anyone
tried to see if the car will fit on the auto transport?

Thanks in advance for your response.
Brian Webber
bwebber@southeast.net