We had a willow tree which was thirsting for water and unbeknown to us, the roots grew right up our drains and blocked them completely last summer. The stench was awful and first drew our attention to the problem. It cost us a lot of money as we had to have all new drains!!!!!!They are not good tress for gardens unless they are very far from the house or, as the first person said, near a river bank. If your neighbour has done something to them then they have done you a BIG favour. Maybe they were worried about the problems which the trees could cause for them. Get rid of the other one too.