I think the idea is that a lot of grammatical knowledge comes down to an eye for detail and a desire to appear professional. Think about its vs it's. If you didn't just brute memorize which to use when, you could work it out with a moment's thought. Yes, it's odd that a branch might simultaneously be the tree's branch and its branch, but if you think about it, its fits in with hers and his. On the flip side, if I'm shortening 'it is' then I really do need that apostrophe to designate the contraction. The ability to do that kind of thinking (and the willingness to apply it to things which might appear trifling) is an important job skill generally. I am slightly concerned the author might not include speaking AAVE an extenuating circumstance (which I think is what matdesigner was alluding too when he mentioned racist issues), but I'd rather not damn him for that until I actually see wrongdoing.
Well, with something of that magnitude sure. There's obviously a huge difference between "it's" and "its." I felt like the boss in this scenario was being much more strict than that.