I think Waitrose's excuse is rubbish. a pie is one item of food, chips are another, mash another. They can have a seperate allergen list for each. If a customer has no allergies and says so, (possibly even signs so), what is the problem?
In our family we have members with allergies and one has an epipen, so I do understand the problem. At Christmas we all ate out. The waitress asked about allergies the first time she came to the table and then brought us an extra menu that listed all the allergens in every dish. This included side orders, like extra chips, mash, onion rings etc.
We ate confidently because we knew exactly where we were. Our order included me swapping mash for boiled potatoes.
I think Waitrose's explanation was a sign of laziness and lack of constructive thought.