You will be pleased to know I am an instructor and examiner
Yes. But are you a lawyer?
There is nothing, that I can see, in the rules that specifically permits a passenger (as opposed to a PUT) to 'have a go at the controls', but there are sections that can easily be interpreted to mean that it is not allowed.
To reiterate: I think it is great for passengers, flying with a friend, to try out controlling the aircraft - to any extent that the PIC is happy with.
However I do not currently want to see this tested in court because I think the rules, as are, say it is not allowed. Unfortunately I think a court case is now much more likely: An, unknown, member of the public who wants, sees advertised, books, pays for and expects "an air tour of short duration" but is then offered the 'opportunity' to fly the aircraft.