Ok, let's take what London said;
Some guy throws a sloppy haymaker at you with his right arm, you "dead arm block" him with your left forearm, you then simultaneously slide your left arm over and around his right arm at the elbow joint and place your right palm on either your attacker's right shoulder or throat (depending on the length of his srms and yours) and place your left palm onto your right forearm. from here a simple flexion at your left wrist joint will create a standing armbar on your opponent and render him not only complacent, but also very easy to move around (since they will be up on their toes) and you can use them as a human shield against their buddies (should your friends for some reason let one of them approach you). All of this occurs in a fraction of a second and your opponent will be more than happy to tell his buddies to back off due to the intense pain he will be experiencing the whole time you have the lock on.
Now obviously this takes training to pull off and won't necessarily work against a skilled boxer (but them most skilled boxers aren't going to throw sloppy haymakers at you in the first place), but against your average "tough guy", the shock and pain of feeling his radial nerve getting smashed between your ulnar bone and his radial bone is going to create a momentary stun or lapse in his attack and give you the time required to do the rest of the movement.
Or, my preferred method, "spear" his haymaker (causing a simultaneous strike to his radial nerve and carotid sinus), thus again stunning him (if no KO'ing him), and then (assuming this scenario, and assuming you don't want to simply knee him in the testicles and end the fight right then and there), trace your left hand down to his wrist and reach around underneath his elbow with your right arm, placing your right radial bone behind the Golgi tendon organ of his right triceps, your head on his shoulder (to prevent him from being able to hit you or get to your hands, and simultaneously pull your right wits towards you and push his left wrist in the opposite direction, again creating a standing armbar. He will again be up on his toes in severe pain and thus very easy to move around (if need be), and convince that he should tell his buddies to back off.
The good thing about grappling is that even though you can potentially destroy joints or render someone unconscious with it, you don't usually have to, and once they calm down and you let them go, they have sustained no permanent damage, and in fact there is no physical evidence that you harmed them in any way (better from a legal standpoint).
Now, had it been London's buddy by himself against this guy and a bunch of his friends, then yeah, striking would definitely be my choice as well. I'm purely talking about the situations where you don't really want to hurt someone, but you want to convince them that they don't want any part of fighting you either. For that purpose, grappling is pretty ideal, hence why it's taught to LEO's and security.