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Party wall agreements don't really work like that - ultimately, they cannot refuse consent (or access) based on whether they like the work or not, providing the appropriate procedures and timescales have been followed.
As @EstelleGetty mentions, it can be used as an opportunity for them to protect their future interests, viz. not wanting to build a shitty flashed in box as an example, by having a wall built up (and potentially shouldering some of the costs).
Having an independent surveyor prevents problem down the line - a shared surveyor is a nice idea, but that independence is a coin toss.
I don't think her own surveyor would have changed anything here, unless you think they can insist you build the party wall up with brick which I am not sure they can?