In my, admittedly limited, experience. no one actually steps it up under stress. You step down to the lowest denominator of your training and experience
These days, self-defense training is preoccupied with the concept of "stress drills". In stress drills, a student will have to apply their techniques and concepts under duress in a semi-uncontrolled and unpredictable environment. The objective of this difficult regimen is to accustom martial artists to the chaos of an actual confrontation. Pumped with adrenaline, humans tend to revert to a deeper motor memory, incapable of performing fine motor actions, and cut off from their higher thinking processing powers.
Think of it this way. Everyone gets in heated arguments with their friends and family. We often, caught up in the moment, say things that are mean, stupid, and unbecoming of our day-to-day selves. Looking back on such an incident, we say things like "I got flustered" or "I was mad and didn't know what I was saying". I have done this with both my peers and my family, and have regretted it every time. And every time, I know that I was just making an excuse for why I failed to act under this stress. If you too know that feeling of being flustered, overwhelmed, and agitated, feelings which then guide your subsequent decisions (Bad decisions, I should say), then you understand why acting under stress is hard.
Stress drills try and eliminate those problems in an extra-gym confrontation. Because you have some idea of how a real attack might look, you are way better equipped to handle it. Another way to think of it is like driving a car. You can watch movies of people driving cars and read about it all you want. But until you actually get behind the steering wheel, you have no real experience in it. Moreover, once you are steering that car (As most 16 year olds know) you are not nearly as skilled as you think you are.
The same is true of martial arts. In my, admittedly limited, experience. no one actually steps it up under stress. You step down to the lowest denominator of your training and experience. If you have gone through enough training and practice, the right kind of training and practice, you can at least make sure that your lowest level of training is suitable for the fight at hand.
The point to reflect on is not just how this applies to martial arts or self-defense. Rather, you should apply it to all parts of your life. Say dumb things in arguments? Practice arguing so you keep your cool. Lose your train of thought in public speaking? Gather a group of friends and figure out how to keep it together. Getting too stressed on dates? Go out with a close female friend and try and simulate some of the process. Stress training is not just about self-defense. It is a good life skill that can help you act under any and all forms of stress.