Assuming you've properly secured the database, that won't be the case. If you've properly secured the database and they attempt to open it with a different workgroup (like thier own System.mdw file) then they will get the "You don't have the permission blah blah" error message.
User Level Security consists of a Workgroup file and the Database file. The Workgroup contains Users, Groups, User+Group associations, and Passwords. A single workgroup can be used to secure many different databases. The database file itself contains the object permissions - all the workgroup really does is authenticate the user, and then pass a SID to the database, which that db then uses when determining the actions a user may take. ULS is also "session-based" - that is, I can have multiple "sessions" of Access open on my machine, each using a different workgroup file. If I have SessionA opened with WorkgroupA, and I attempt to open a database in that session that was NOT secured with WorkgroupA, then I get an error message (assuming, of course, that the database is properly secured).
In order to open a properly secured database, you MUST use the workgroup file that was used to originally secure the database. To do that, you have two choices: either join the machine to that workgroup (NOT a good idea), or use a shortcut as described above to open a session of Access with that workgroup. By far, the better idea is to use a shortcut to open a session of Access.
As to the DB password - I didn't see that, since it highly unusual to have both ULS and a database password - then once you open the database you can use DAO to change that password:
CurrentDB.NewPassword "old pw", "new pw"
Of course this is a DAO method, not an ADO method. To do that, you must use an ALTER SQL statement. See this KB article:
http://support.microsoft.com/default.aspx?scid=KB;EN-US;q304915
