Conflicted Copy different scenario without a solution

Since OneDrive might be more integrated with Access, given that they're both Microsoft products, it's possible that they have workarounds built into their systems.

For Dropbox, opening an Access database, while already open elsewhere, would result in a conflicted copy since the act of opening a database could write information to it (such as logs for the last date opened, or an archive bit set as you mentioned). As such, there isn't a way to avoid conflicted copies when this occurs. 

There is, however, a feature on some plans called file locking, which prevents other users from editing a file while it is locked. Only the person who locked the file, or team admins, can edit it while the file is locked. Perhaps this might help out in your situation, since the operator can lock the file and edit it, and the office individual can still open the file to view it, without writing anything to the file. 

While this does work for normal single files, it should also work for databases (if they don't expand into subfolders that are visible on Dropbox), so I would recommend testing it first, just in case.