You can get those [not being able to update] messages even though there are no broken links... searched a workbook many times, but there's none [not even in named ranges that contain a dynamic formula].
Of course, linking to files with the same name is asking for trouble, and the last warning screenshot confirms so. Would you ever open that archived copy, it will substitute links to point to itself.
One pit-fall is using certain methods of index/match with offsets to fetch data from an external book. You could end up with #N/A evaluations, subsequently followed with warning of errors.

EDIT: An example what does work, where the name\location of the file can be changed by making indirect look at a secondary field to get the file name [in text form]. Sample

=INDIRECT("'[WhateverFileName.xlsm]SheetName'!RangeCellName")