But..... Yea. Right. Do that. Particularly if you have lots of free time to devote to that enterprise. Better yet, take a few days off your busy schedule to handle the matter. You'll feel good about yourself and the fact that you did your civil duty.
The key is that you probably won't have to do this once they know you won't grovel...
We typically give the benefit of the doubt, even if the customer seems scammy, as long as we can see a point where we might have done something differently along the way to avoid a misunderstanding.
When someone threatens bad reviews to get free services though, I have that conversation with them, even offering to send them some clips of court rulings. The potential embarrassment of being exposed and having to publish apologies is usually enough.
One person carried through with the bad review threat and posted a hatchet job. I answered the posting with the details of their extortion threat. There was a pretty long list of pro-Burns comments on the post, so with that review neutralized there was no need to take it farther.