Its a line from quite a few stories and anecdotes, about people who come out of stressful situations, having been around the dead and dying and what not, with their hair turned grey in just a few months, or one or two years.
Can stress do this to a person?
My guess would be no. Genetics is the key. I’ve been stressed for years and have little grey hair to show for it. Coincidentally my dad never had much grey hair either.
Related from Cecil: Can hair turn white overnight from fright?
Synopsis, not really, but stress or fright can very occasionally make all of your hair that hasn’t turned grey or white already fall out rather suddenly. Read the whole column for full details.
ETA: Somebody already posted the link I was gonna post.
Wow, I’m think I’m somebody! 
Anecdote isn’t data but …
I went from the same dirty blond color I had at age 5 to solid grey in ~18 months at age ~32. Nobody else in my family male or female is, was, or has since been an early turner-grayer.
Those same 18 months I built my first start-up. 15 hour workdays 7 days a week for 18 months.
Now 20 years later my hair is the same color it was when it finished turning back then, and is just as thick.
Could be coincidence. It wasn’t the first time I’d busted ass for a year or more; it was however the hardest.
I’m one of those “prematurely grey” types. Just two weeks short of 30, I’m solidly salt and pepper. People have been telling me I have grey hairs since I was in 9th grade (about 14 or 15). It’s something I get from my mother’s side of the family. Based on my experience, I’d say genetics are an overriding factor (much like with baldness, which I am fortunate to not show any signs of).
Well, my mom had curly hair as a child, got Scarlet Fever, it fell out and grew back in straight.
Myself, I get alopecia areata every few years or so. A patch of hair falls out, grows back in white, then gradually returns to its normal color, which these days is increasingly grey. The docs don’t know exactly what causes it, but stress could sometimes maybe kinda be a factor. How’s that for a factual answer? I’m proof hair can abruptly change color. Not the hair that’s already there of course, but the new hair growing in.