@Neil
1) Which version of Word do you have? I just typed in your sentence (added "the" at the beginning) and there's absolutely no issue.
2) I get the feeling that the beginning of your sentence is what made Word trip up. Happens sometimes, depending on how complicated it is (haha).
3) Here's a lengthy post about Word's spellchecker options (plus examples). You can change quite a bit--if you have the time, that is:
https://support.office.com/en-ie/article/select-grammar-and-...@Charles
Wish someone had posted an explanation like yours--"you are using it as a plural and not a possessive" is not...very illuminating.
Never mind that there are plural possessive nouns (whether that's correct in this context isn't the point).
Best wishes