Competing in MMA is not for the faint of heart. It takes dedication, sacrifice and maybe even a few loose screws. The commitment associated with stepping into the cage is something that few can understand.
And because of that, no one—even the referee—should be able to decide when a fighter chooses to submit, except for the fighter himself/herself.
Let's be clear; opting not to tap to a choke, armbar or other submission is not the smartest idea for anyone. However, just as fighters make a choice to step into the cage, it is their decision whether or not they want to face serious injury.
Take, for example, Brazilian jiu-jitsu black belt Antonio Rodrigo Nogueira. The heavyweight was both too stubborn and proud to tap to Frank Mir at UFC 140 (see the above picture). "Big Nog" paid the price with a broken arm and a lengthy recovery period.
In that fight, referee Herb Dean waited until Nogueira's right arm was mangled before intervening—much the same way that Dean had waited at UFC 48, when Mir snapped the arm of Tim Sylvia.
The role of the referee is to maintain fighter safety—meaning they enforce the rules and prevent life-threatening injuries. They are not to decide whether or not a fighter wants to continue trying to escape until the lights go out or a bone gives way. Again—for clarity's sake—it is absolutely the referee's job to step in once a fighter is unconscious or has suffered a significant injury, such as Nogueira's.
Although the consequences of neglecting to tap are quite clear, the punishment that fighters' bodies endure is something that they elect to put themselves through. If they choose to subject their bodies to broken limbs, torn ligaments and other serious injuries in training camp, the referee is right to let them do it inside the cage on fight night.