One other issue to check, and you didn't describe it but I will give you a forewarning:
Everyone who will be using a database with split FE/BE will need "MODIFY" permissions on the folder and all files therein. Which is why each shared database really should be in its own folder. Note that there are TWO levels of permissions - the broad-brush categories such as READ, MODIFY, FULL CONTROL, etc. - and over 20 individual permissions such as "Pass Thru" "Read Attributes" "Write file" etc. When you right click on a folder and look at its permissions, the broad-brush options show up and you can just choose MODIFY. You don't need to go "Advanced" to get to the detailed permissions.
The reason you would have a read-only database or other exclusion is that if the FE copy (that is on the end-user's machine) is unable to create or modify the .LDB file in the same folder as the BE database, then you can't lock anything so it opens READ ONLY.
The inability to open the DB at all points to the Exclusive mode problem, but often if your IT department is being a bit prissy, you will run into the permissions problem.
As to "Our IT department does not support MS Access." ... I hate to break it to you, but they have nothing to support except sharing permissions. A "pure" Access (i.e. both FE and BE are .ACCDB or .MDB files) is just another app that shares files. Excel and Word allow "collaboration" even if they don't allow simultaneous editing. If your IT department sets up shared areas with permissions as described, that is really all they can do for you. Access goes the extra mile on its own. So other than assuring a decent file sharing setup, don't be too hard on the IT department as long as they don't get in your way.
If you search this forum for articles on database permissions, you might find some other useful discussions on this subject.