Excel says file is unreadable in Read-only, but the file is fine in normal mode

Question

I've done extensive research and tried re-installing Office 2010 a few times, but I cannot seem to be able to open files in Read-Only mode in Excel. Whatever the extension (xls, xlsx, xlsm, xlsb...), it does not matter, they all give the same error. The problem started a few weeks back, but I have no idea why.

When I open the file without Read-Only mode, it works fine. But when I try with Read-Only mode, it give me the following error: Excel found unreadable content in package [FILE_NAME]. Do you want to recover the contents of this workbook?

Before you think the file is corrupt, please, that's not it. If I open Excel, type value "1" in cell A1, save the workbook as test.xlsx, close the workbook, then re-open it as Read-only, it gives me the error. But if I open without Read-Only (normal mode), it works fine!

Any ideas from your experience will be greatly appreciated.