dBaseIV uses "production index files" that get created automatically when a datafile is created (.dbf file). It has the same name as the datafile and an extension .MDX. The datafile has a flag in it's header indicating that the production index exists. This will automatically open that production index file. Sounds like that's what you're running into. (Single index files and independent multiple index files have to be explicitly opened.)
If the DOS app needs to continue to use the index file, I'm not sure there's a way around the index. If the app is something you're abandoning/converting and thus don't need the index file in the long run, I'd be tempted to move the .MDX file to another directory, then hit the database with Access and see what happens - quite possibly an error. If that happens, then I'd open the .DBF in a an editor and see if you can spot the flag for the index file in it's header and change/delete it. I've not done this before, so I'm no help in what the flag is or how it appears in the header.
If it's dBaseV, things may be entirely different - I have no experience with that version - maybe someone more knowledgeable than I will help. There are probably ways of using Visual Basic or other tools to connect to Dbase and ignore the index - I'm just not familiar with them....
Sorry I couldn't be more help. Good luck.