As both an individual who has suffered from bipolar disorder, ptsd, anxiety, panic and an other disorders at various times in my life, and also a highly intelligent woman who has studied psychiatry and medical courses in college, I can tell you an answer from a very different perspective. My answer is that this is a false assumption! There you have it.
The complex issue of a mental disorder cannot be broken down into strength or weakness of ones constitution, or a mind over matter thing. The brain is seven pounds of white and gray matter with complicated sections controlling many of our functions, or rather all of them, utilizing chemical neurotransmitters and electrical impulses. Through these channels (basically neurons, dendrites, and axons) our brains chemicals are passed through and used to control its functioning on a daily basis. Some of these chemicals assist with our mood and others stabilize our feelings in other ways, and some even cause food cravings. However, shortages of some of these chemicals, i.e. dopamine, norepinephrine, seratonine, just to name a few, or the damage to the way that they are taken up by the dendrites to the axons in the brain will cause an inconsistency in the proper levels of these chemicals in the brain.
In this case, individuals can have issues with mood swings, sometimes severe, either one way, the other way, or both causing disruption in their lives. Therein lies the problem and thus medication is needed to supplement this chemical disruption in the brain. Much is still not known about the brain and its function, even though we have had one in our craniums since time began, but progress is being made. We have amazing neurologists, neurosurgeons who can blast a tumor out of our heads, and yet still when it comes to a mental illness that it comes down to the seven pound organ in our skull being out of balance, there are still people in the "dark ages" who still would like us to "control it ourselves" by "mind over matter" control.....uh.....not gonna work.
I am in control and stable on a mix of topamax and wellbutrin xl daily and live a truly productive life.
Good luck and hope this answer was not too thorough!