Short answer:

Nope, that's unlikely to be true.

Discussion:

Mental health is treated substantially differently in Japan than in the West, and things that might be characterized one way here might be called something else, or not spoken of at all in Japan. In particular the Japanese have a social ethos of stoicism, the so-called "gaman spirit". There are common Japanese phrases that we usually translate into idiomatic English as "good luck" ( gaman site kudasai or gambatte ); translated more literally the words mean "please endure it" or "tough it out". That tells you something about the approach to adversity in Japanese culture-- speaking up about it isn't encouraged. So they might not have a diagnosis of PTSD where we would and you're unlikely to find a statistic that would let you make direct comparisons of Japanese vs other veterans, but everything we can see suggests a lot of trauma.

Japan had and still has a high suicide rate-- including many suicides of those with military service, though I can't find that broken out in the statistics that I can access. The rate was much higher in the post war years than at present, and many more men than women. Most of the suicides of men in the late 40s and into the 50s and perhaps even the 1960s would have been men with military service. How are you going to disentangle their veteran status from other causes, when veteran status was so ubiquitous in these cohorts?

We have many Japanese memoirs and films made by veterans that reflect a desperate wartime experience and profound stress. Two examples that come immediately to mind: Kike wadatsumi no koe ("Listen to the voices of the Sea", from 1950) about the Japanese defeat at Imphal. It's pretty desperate stuff, and was based on the writings of Japanese students conscripted as soldiers. And most recently the 1987 documentary by a veteran of the New Guinea campaign, Yuki Yukite Shingun ( in English it was "The Emperor's Naked Army Marches On") is a first hand account of trauma that 40 years later was still pretty brutal.

As to war criminals -- many of the more notorious were unrepentant and unpunished. Prince Asaka, the commander most responsible for the Nanjing Massacre, lived out a seemingly untroubled post war life as a golf course developer (General Yamane, a much more sympathetic figure, but one who didn't have the advantage of being the Emperor's uncle, was hanged). Naito Ryoichi, a physician associated with Unit 731, which carried out medical experiments on Chinese prisoners -- he went on to found a pharmaceutical company. One of the Japanese to openly discuss participation in war crimes was Azuma Shiro, who wrote a memoir of his military service, and traveled to China to apologize. He appeared to be deeply traumatized.

See:

Wilson, Sandra. “Film and Soldier: Japanese War Movies in the 1950s.” Journal of Contemporary History, vol. 48, no. 3, 2013, pp. 537–555.

J.J. Orr, The Victim as Hero: Ideologies of Peace and National Identity in Postwar Japan (University of Hawaii Press: 2001)

Azuma, Shiro. "The Diary of Azuma Shiro", [2006]

The art of perseverance: How gaman defined Japan -- not academic, but a good introduction into gaman as a cultural norm.

The most recent English language sociology/anthropology introduction to Japan that I've read was

Sugimoto, Yoshio. "An Introduction to Japanese Society", (Cambridge University Press:1997) . . . there's likely something more recent on the subject, but one virtue of being twenty years old is that it's much closer to WW II.

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