After a bit of digging, I think his story is plausible. He got into the game in 2004; At that time, it was very much possible for a smart, determined teenager to grind a hundred bucks into a quarter mil. Before Black Friday[1] chased all the soft money out of the game, pretty much anyone with an ounce of sense could play profitable poker and some people made a lot of money very quickly. He claims to have blown most of his winnings in that one-month losing streak, which is very much a thing that cocky 18-year-old poker players do.
I think it's fairly clear that Meyerson came from a relatively privileged background and had a lot of advantages - he attended one of the best high schools in the US - but I don't think it's necessarily fair to dismiss him as a trust fund kid who lucked his way through life.
[1] https://en.wikipedia.org/wiki/United_States_v._Scheinberg