The bar raiser can say "no" even if the HM says "yes," but I never heard of it going the other way (where hypothetically the HM would say "no" and the bar raiser "overrule" the HM.)

And in hundreds of interviews there, I never experienced a situation in which it was as black and white as the above would make it seem. There were times, of course, when there was a difference of opinion, but it's on the people in the room to debate and convince each other based on logic and data - a bar raiser is not simply going to walk in and put his/her foot down and say "no" to a team that is otherwise saying "yes" without pretty detailed discussion and reasoning.