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I had a party wall thing a few years ago. I don't think you need to give a reason for an independent surveyor, they're obliged to provide that as an option.
From memory, the options you received on the party wall notice are 'consent', 'use same surveyor as neighbours' or 'use independent surveyor'.
I don't know why anyone wouldn't choose an independent surveyor (from my experience I'd definitely advise it), but you don't need to provide a reason for your choice and whichever you choose the neighbour is obliged to cover the cost.
Thank you @ectoplasmosis @Brun @Grumpy_Git