I think it's a very complex issue and has very little to do with the rigors of training. If I had to venture some guesses:
1) Highly intelligent individuals with mental illnesses often go undiagnosed because their intellect allows them to function where others couldn't.
2) Substance abuse often goes undiagnosed in intelligent people.
3) Admissions selects for hard working, driven people who have known little or no failure in their lives. No, 2 weeks on a mission in Africa is not adversity, especially if you got bumped to business class thanks to your parent's FF miles.
4) By definition, half of the admitted students who have been accustomed to being at the top will instantly become "below average."
5) Most people in medical training are NOT brilliant. Intelligent and hard working, yes, but brilliance is still rare and those who have it are the rockstars who glide through effortlessly wondering why everyone else has a problem. Many will be working consistently at the limits of their intellectual ability.
6) Most students, especially traditionals, have very little support structure for either med school or residency. As a result, coping may not be ideal. See #2
7) Substantial debt burden makes quitting not seem like an option.
I think non-trads are probably less likely to fall prey to suicide for many reasons. They've had more time for underlying mental illnesses to come to light, they've experienced real challenges and adversity before, they don't define themselves by their scholastic achievements, they often have family support, etc. That maturity and experience of dealing with stress is a huge help. We're don't like rejection but we've accepted it as part of life. We've screwed up plenty of times and had to work past it. Many traditionals -- including the two suicides mentioned in the article -- are having to adjust to the realities of the professional world AND learn medicine at the same time.
No easy fixes I'm afraid. The biggest fix would be at the admissions level, perhaps requirements for 1-2 years of full time work, although the whole process takes a long time as it is. Perhaps more weight given to MCAT scores than GPAs as a means of selecting more people with innate intelligence versus the people working hard to compensate for average-or-less intelligence. I know that sounds awful, but there's no way to sugar coat the idea and we're all grownups here.