Your point is stupid and completely off the mark.
Even if we start from the same premise, that neither sport is the sport of fighting, one sport is clearly a far superior proxy for fighting than the other. So much so, that to bring one up in the context of another is ridiculous.
I suppose I'd like to hear your definition for fighting though. If fighting has aspects other than striking a grappling I'd like to hear what they are.
In real fights people have guns, knives, weapons...there are no 'weight classes'.. hair pulling, groin strikes, punches to the back of the head, biting are all in real fighting..depending on the environment, the hard floor means you can smash someone into the ground far harder than a grappling mat or a fight canvas... the surroundings completely alter how you would otherwise fight..and people jump in and out, you punch a guy, his friend punches you, your friend punches him etc etc.
Neither MMA nor Boxing are anywhere near real fighting. Nor does succes in one mean that one is a good 'fighter' , just that they are a good competitor, or, ring fighter if you will. Shinya Aoki and Floyd Mayweather would both get there ass kicked by tons of heavier, bigger, prison inmates, despite that they are both excellent ring fighters.
My point is NOT to insult MMA or Boxing (or Wrestling or BJJ) I LOVE combat sports with all my heart, but not because they 'prove who would win in a fight, but because they show incredible athletes performing to levels of skill unattainable in 'real fighting'. I love Boxing because Punching, as an art, is beautiful to watch at a mastered level. Floyd Mayweather and Naseem Hamed are artists in Boxing, but in 'real fighting' they would never be able to perfect such punching. Likewise, in MMA, fighters like GSP, Anderson, Aoki, all demonstrate incredible skills in combining striking and grappling in a cohesive and tactical fashion in a fair regulated sporting environment that is not possible in 'real fighting'.
On the street, if I had a gun, I could kill Alistair Overeem. The purpose of 'ring fighting' is to show us who has developed the highest level of athletic combat skill, not who is the 'baddest man on the planet(A term which should be labeled 'Baddest Man on the Planet in a controlled sporting environment'.) Ring fighting is sort of like an idealized fantasy world, its a 'what-if' scenario.
When the guy I first quoted tried to put down Boxing as being 'less real' than MMA this is my viewpoint on his viewpoint.