There's two possibilities.
1- It's within Access, but you'd notice this because you were using the built-in Access security module and the user has to login when opening Access (although it's possible to set this once and not do it again)
2- (and more likely) It's a network rights to the folder where the mdb exists that is the problem. If true, the read-only message would show up when they attempt to open the database but before they can see anything.
The problem is, Access creates a temporary lock file (ldb) that exists as long as anybody has the database open. If it can't do so, (user doesn't have privs) you can't open the database.
Copy the database to a folder they control and see if they can open it from that location.
Mike
