I definitely agree, the customer is not always right, but because of the way he reacted and it being on social media will cause him more business loss than had he not got all crazy.
Neither side was professional in this situation. She should have expressed her irritations either on the phone or in person. Then if she really needed to write about it she should have written her concerns on YELP. Doing it on FB made it seem like she was trying to get something free. The person responding for the restaurant is an idiot. He should have responded to her politely. Bad reviews are going to happen, but being a jackass to customers is never smart online (this is a huge audience). Plus had he been cordial and commented without attacking, her true motive would have shown quickly and people would have ripped her a new one.
my .02