Do you have a contract on your property? If not, you need one immediately with a clear and defined cancellation policy. Myself and most other owners on this forum would never refund in full to includes taxes and cleaning on the day of check in. I think that this gives renters a sense of entitlement to think that they can book a property, the owner holds the property for that person and then refunds the renters on the first day because they are unhappy. This has appeared to happen more than once so you might want to check to see what is making these guests unhappy. What kind of negative comments are they saying that you say are untrue?
As to them renting from your neighbors, they only did this because they were relieved of their obligations at your property. Maybe your prices are not in line with the expectations of the renters and when they get there they are disappointed.
At some point, us owners need to have a backbone and stand up for what is correct and not let renters walk all over us or bully us.
I wonder if you have a competitor who is somehow intercepting your guests when the arrive and telling them you will refund their rent if they complain and then they can rent their place for much less. I would never allow them a refund unless the property can be re-rented and that isn't going to happen if they pull out the day they arrive. One negative review out of 50 would certainly not cause me to reject a rental. Most people realize there are people who just cannot every be pleased.