首先说明如果单独用They have left the girl by themselves.这句话并没错.可解释为：他们按照自己的意愿留下那个女孩.（主观色彩很浓）
by oneself:单独, 独自;出于...按照...的意愿
for oneself：表目的
of oneself:adv,自动的,相当与automatically
既然有前句They have left the girl alone .那么同义句当用They have left the girl by herself（此处leave有所不用并不是单纯的离开,而是构成leave someone by oneself(alone)的固定搭配.