First things first: If you want to convince your Owner that it is the prudent course of action to respond to a negative online review, do your homework, such as reading Nate's link and reading research done by a reputable multifamily associate, such as Satisfacts. There are many blogs and authorities that tell us it is better to respond in a neutral manner, without animosity, to a negative post. You need not go into a lot of blather or detail either in your response. I believe Mark Juleen posted a great response on Multifamily Insiders about this. In fact, I would just show your Owner this site!
Second, you can always ask happy residents to post their thoughts on living at your community on line, too. If you are 98% occupied and are always highly occupied, I would not worry excessively over this one nagative review.
And finally, I would not think there is something wrong with the staff if there is no follow up to ONE negative post. I also would not presume to think no one cares. Sometimes, there should be no public defense which may make more out of something than needs to be. I think your Owner may feel like this ... he is concerned that a very defensive reply will look like a there is credence to the original negative post.