Hi Stephe
I very much doubt it's anything to do with the end-users machine.
Sounds like it might just be a bug
Or...
Does this work sometimes and not others?
If you give Read access, but not update or delete, do those policies work correctly for the second user.
Was the second user, by any chance, a super administrator - if so, they might have special privileges that mean that he can access the file even if a "normal" person can't.
Howard