My first thought was maybe this was SSMS bug and nobody could do this. But just verified that I (a sysadmin) can script out definition of such a table type.

I don't know answer, but expect you could find it pretty quickly by running profiler and filtering so only see this one person's commands, then have them repro the problem. Include RPC start/complete, SQLBatch start/complete, most/all error/warning events and oledb errors. I expect you would see at some point a command followed by an error msg, which hopefully guides you in right direction.