The updater replaces the old version, unless you're saying you have people making copies or renaming the database file?

That sounds kind of rough to have a foolproof solution. The first ideas that came to mind were windows settings/gpo or registry edits to control trusted locations/files, but that's probably overkill. You could probably just make a table that stores the file name of the new database and mark it as IsCurrent with a yes/no field. Then check for the name of the file being opened when the database opens in the on load event of the main form. If it's not correct kick them out of the database, or delete their file, or launch the udpater, whatever you want to happen.

The file name remains the same.  In my case, DFM1.accdb.  Application Title changes.  In my case, Access Updater DB v.127.  Could it be done by checking the Application Title?

Sure, you can just check for the application title on open and make sure it matches.

MsgBox CurrentDb.Properties("AppTitle")

Could you put a field in a system or hidden table in the back end that maintains Version #?  Check the FE version with the BE ver via the updater.
If it isn't correct shut down.

Ultimately -  If someone really knows access they will be able to get to your data.
If you really really need to secure the data the best way is to move to SQL Server.

How likely is what you are discussing? You have to ask yourself, "Am I just being paranoid or do I have a legitimate concern?"

At this point, I'm just taking another step in locking the database down.  I'm not concerned with a real Access hacker breaking in.  Prior to making some security changes, I only had the BE encrypted with a password.  Turns out (of course) the table can still be accessed and changed.  And that is what happened in my case. Someone changed a table which altered multiple records.
So far my database is split, the Back End is encrypted with a password, the Front End opens to the Main form which runs the code "   DoCmd.ShowToolbar "Ribbon", acToolbarNo".  This prevents them from going to File>Options and changing things back.  On the Option menu, for the FE it has the Navigation Pane, the Use Access Special Keys and the Menus turn off.
I'll see if I can figure out the MsgBox CurrentDb.Properties("AppTitle") to check the app title.
Thanks for the help.

The only way I could see doing this would be to encrypt the data in the back-end table and changing the encryption scheme in each new front-end. Let them convert the data once when they upgrade and then they can no longer read it with the old database. Access Data Encryption Seminar