I can kinda see your point but the onus is really on your to prove to the police you have permission and if you are unwilling to get it put in writing then you can understand that you are making both their job more difficult and making things more awkward for yourself too. It isn't a requirement of law but more a case of being the respsonsible thing to do so that it makes everyones life easier (you, the landowner and the police).
I had one farmer that although he gave me verbal permission I was struggling to get written permission off....he was just old fashioned. So I did tell a white lie