Only because this was an issue for several people over the last year who called us...note the following:
Older Access databases end in .mdb (Access 2003 or earlier)
Newer Access databases end in .accdb (Access 2007 and later)
If you compile a database (Click File, Save As, choose MDE or ACCDE) you are turning it into a file which can run without someone being able to go into design view.
If you ONLY have the mde or accde file, you can not rename it to try and trick access (renaming an mde into a mdb does not work). You NEED your original file (the mdb file) in order to go get those tables and change up the design.
In the case above, we had a client provide us with an MDB file which we were unable to successfully open. The error was incompatible version. After trying ALL versions, we finally found out the client had actually renamed their MDE file to try and edit it. sigh.
I generally do not use mde or accde files, though they definitely have their place and time. Our projects tend to be very fluid and dynamic, we like being able to rapidly make changes for short notice requests without having to redeploy a new accde file.