因为这个状语不是主句的状语,而是定语从句中的状语.另外,on the edge of which这个介词短语也是定语从句的状语.
给你几个从句中介词短语作状语的例子：
I don't know why,at this late moment,he is still resisting the idea.
We went to the zoo today where,for whatever reason,everybody went.
It was an idea that,at that time,was too new for him.