is it up to the check in staff to do this by them self?

Surely it is CBP to determain the valididty of the document

Was he just visiting the US. If if was good enough to alow entery then it's funny not to leat him leave.

I know of someone detained on entery to the US due to a damaged passport while custems cheched out the identiy of the person, after discussion with thier consulite they were admitted.