I might come across here playing devils advocate, but bare with me.
Did you SS tell you what Dad said or have you and your wife talked to him about it? You've already said the son can stretch the truth a bit, so maybe there is more to this story. Could Dad be offering to teach him to defend himself and just be talking a little tough in the process but not really meaning he wants to knock the kid off his feet? I can't imagine a Dad who was told by his son he was bullied, came up with a plan of action, (regardless if we agree with it), willing to buy gloves and take the amount of time to teach him to defend himself, and to be calling over and over to get the kid to talk to him not caring about the boys welfare. Perhaps looking into it a little more might clear things up. I wouldn't let a grown man hit my child with a grown mans full force, but I would let him teach him to defend himself. A person should be taught to walk away if they can, but sometimes you can't walk away. Knowing how to take a punch and land one can make a big difference in the future. All mine, girls and boys alike were taught to defend themselves.
And if the boy is just crying out for attention, well... he's gotten it. Might be a good lesson in if you cry wolf there are consequences. We are taking is seriously, talking to teachers, coming up with a plan of action and so on. And if he'd not making it up, then a little round with Dad might make him realize that doesn't have to be a punching bag for some kid at school.
Talk to the Dad. If its just a case of boxing around the front yard to build some confidence then I don't see how it would hurt.
My oldest boy was a runt. A foot shorter than all the others his age and scrawny. He took a a$$ whopping everyday he went out to play from the neighborhood boy. Talking to his parents did nothing. Forbidding the kid to come in my yard did nothing. My teenage brother and a new pair of boxing gloves for a few weeks gave Adam the push he needed to stop taking it. The day I heard the bully screaming and had to pull my son off his chest where he was sitting while pummeling the kids face was the last time he ever messed with Adam. Sometimes, you can't just turn the other cheek.