Grammatical Error on New “Apocalypto” Poster

The new Apocalypto poster boasts this slogan: No one can outrun their destiny.

To which Steven Greydanus responds,

Shouldn’t that be “No one can outrun HIS destiny”?

Other grammatical alternatives:
“No one can outrun destiny.”
“You can’t outrun your destiny.”
“People can’t outrun their destiny.”
“Outrunning destiny? Fuggetabbatit.”