You can't make everyone happy. Sometimes no matter how hard you try someone will always find something to complain about, be upset by, or just not like. You know this is true in your everyday personal life, so it stands to reason that your business will eventually, have to right a wrong, even if it isn't actually a wrong.
People are funny. Some know that you can't jump quick enough to make them happy, while others always feel slighted and have to let you and everyone know. And, since we are human, we all make the occasional mistake. So, whether the negative feedback is valid or not, the way you handle it should be consistent and could mean the difference between sinking or swimming.
Never feel that negativity is the end! Don't lose sleep over it! Don't shy away or delete the negative comment. Face it head on. Addressing your customer in a public forum is never the best way to handle a tense situation. Apologize quickly, than take the action private with a private message to the customer but a public message that you are sorry and that you have sent them a message and want to fix it.
This shows your customers and potential customers that you are considerate and want to diffuse a situation. Plus, your customers may feel the need to come to your defense which is always a good thing. Turns that negative situation right into a positive one.