Short description of error
Blender tends to get very confused with relative paths when files are higher in the directory structure than the .blend file itself.
It sometimes gets paths that go all around the hard drive (\level1folderA\SubFolderA\..\..\level1folderB\). This used to break a lot of links in our project because the filepath would 'wander' outside of the Shared directory structure onto collaborator's personal drives.
Finally we had to switch to a shared drive letter to overcome the problem.
Here's some filepaths for textures that I found in our project (I've replaced some foldernames with <replacement names>):
..\..\..\..\..\..\Dropbox\<company>\Models\..\..\..\Google Drive\<projectname>\Art\Textures\Generic\Band_steel.png <== Yes, this one first goes into a dropbox and then back out and THEN onto the google drive
Once the filepath leaves the project folder it breaks for everyone else because they don't have the same directory structure beyond that.
Exact steps for others to reproduce the error
One way I found to reliably reproduce the problem is to use the 'Make paths absolute' function on a relative path that has "\..\"s in it.
To be honest I have no idea how exactly the examples above happen; just that they do frequently enough to make relative paths unusable for our project.