I have a similar issue. We have three computers that are networked together to work on InDesign pages. Permissions are set properly.

Every time one particular computer opens and saves a page, it will become a “read only” when either of the other two computers open it. So we then have to save it as a copy and then delete the older version of the page. This is infuriating, and has more than once led to us losing work because the wrong version of a page was opened or saved. This has not always been the case, but began a few months ago.