You and OP are defining it the wrong way.
DEFINITION of 'Gambler's Fallacy' When an individual erroneously believes that the onset of a certain random event is less likely to happen following an event or a series of events.
It exists means there are people who erraneously believe that.
You are trying to catch me out on a grammatical technicality. Yes the fallacy itself exists, but it NOT an accurate representation of reality. Ergo, it is not true.