In theory, yes, he's competent - but in practice, many doctors won't see them. There's also navigating hold systems when they may not have enough call time on their phones, dealing with reception, etc.
I've got a whole load of additional irritation reserved for the multiple pharmacies that refused to dispense my then 15 year old's prescription for the Pill (prescribed for heavy and extremely painful periods) without a parent present as well - competence is very vulnerable to the opinion/beliefs of the adult the child is in front of at the time.
Anyhow, the OP's son is 'skinny' but not exercising because of back pain. He needs an adult with him to not accept the bullshit 'well, you're a lazy, slouching teen' and actually look into what is causing the pain, whether it is a lack of core strength and poor posture, chronic and untreated injury, a progressive deformity such as scoliosis, EDS or an autoimmune disease such as Ankylosing Spondylitis, Rheumatoid Arthritis, Psoriatic Arthritis.
Unfortunately, it appears that his genuine pain has been ignored for two whole years, so the chances of him getting help other than a 'it's growing pains' sounds pretty low, as anything he says will be minimised or rejected during the consultation.
I hope his GP is better than that, however.
I also doubt the OP will come back and say 'Shit! He's being referred for blood tests/x-rays/physio/the hospital' - it'll be 'nothing wrong, just growing pains and needs to exercise more/stand up straight' if anything.