你理解错了，they do 不能前移。你把非限制性定语从句先撇开不看，句子就简单了：

Soaring tuition costs put them off as much as they do foreigners.

这里的 they =Soaring tuition costs（急剧增加的学费）。所以：

Soaring tuition costs, which have far outpaced inflation, put them off as much as they do foreigners.

=Soaring tuition costs, which have far outpaced inflation, put them off as much as they put off foreigners.

句意：急剧增加的学费大大超过了通货膨胀，这如同吓退外国学生一样，也把他们（应该是指本国学生，与foreigners相对）吓退了。

举个类似的例子：

He loves her as much as he does you.

=He loves her as much as he loves you.