From all of your suggestions, I have attained a partial solution.
The InDesign file we received had a linked Word document that showed up as being modified. If we updated the link, all of the text in the document reflowed incorrectly. So the objective was to unlink this document and avoid the possibility of someone else working on the job would update it unknowing and cause a problem. So we wanted to unlink it prior to it being updated.
As an experiment, I went ahead and updated the link, and then the "Unlink" option did become available in the "Links" drop down menu.
Thus, the link needs to be up to date before it can be unlinked, at least on my copies of InDesign.
However, the "Unlink" still does not show up in the Menu Customization, whether or not the link text files option is selected in Preferences.
As they would say on Myth Busters, the ability to unlink, as far my settings go, is plausible.
Thanks to everyone.