Quote or no quote, Trump doesn't have any patience for the idea of sacrifice or service to others. He's shown none of it in his life, and proudly so. He is what he is. But it's pretty clear the military didn't feel respected at all by him, regardless of what was or wasn't said.
But didn't Trump threaten nuclear war with North Korea at least once during his presidency?
https://www.usnews.com/news/world-r.../north-korea-threatens-us-with-nuclear-attack
It's not beyond the pale to think it couldn't repeat and someone with less resolve behind the panic button wouldn't lose their nerve.
After all, a few months after that nuclear sabre-rattling, Iran blew a Ukranian passenger jet out of the sky thinking it could have been a U.S. missile because of the escalated war situation after Trump drone-attacked Iran:
https://en.wikipedia.org/wiki/Ukraine_International_Airlines_Flight_752
And that's when Trump wasn't feeling threatened of being kicked out of his office. So it's not irrational.