You are absolutely right....
But drawing attention to something this way that would have just disappeared into thin air when left as is.... Now he is the "owner of a restaurant that pursues people when posting a negative comment on social media about his business".
That he is right in doing this will soon be forgotten and does not matter anymore. It is the negative message that stays in peoples memory. People in the long run will not remember what the woman complained about, but they will remember what the restaurant owner did. He better had accepted a public apologie and handle all in peace instead of going to court about some "missing income" which he never can proof. It is better to make the end result a positive than a negative one.
I have seen similar examples happening elsewhere (not in Thailand). And it is always the owner off the business that draws the short straw because he is making the issue bigger than it actually is. Although he has every right in doing this.
Sad it escalates this way. No winners here.