What you are describing is encopresis. He needs to see a doctor, get a diagnosis from a pediatric Gastro-enterologist and start a behavior modification plan. Probably he will need a regimen of Mirilax, but that's up to the doc to explain. His colon is damaged and not working properly. STOP PUNISHING HIM should be your first advice to her, he really truly cannot help it. It will only make it worse.
Kids with this condition lie about it, they can't feel it (damaged nerve endings in the lower part of the colon) and they can't smell it. He is dealing with something that could cause him long-term psychological damage as well.
My son had this, it took 3 years after a diagnosis at age 8 to heal totally. PLEASE tell her to take him to a doctor, you are describing ALL of the symptoms, and there is treatment!
I have helped quite a few moms here with this situation through PM, please contact me if you have any more questions about it. It's curable, but it takes patience and routine to do so.
eta
ok, I see she went to the doctor who is WRONG! I mean, yes it can heal on it's own...like when he's in his 20s! Tell her to insist on a referral to a Pediatric Gastro-Enterologist. Most family docs don't know much about it or the treatment. That little boy needs help, please tell his mom not to give up.