No, but having said this evidence is offers selectively in many cases. Even when parents are represented by legal counsel. It's not unheard of for authorities and counsel to work with one another to get the expected outcome.
There is currently a system in place that is rigorously promoting and focusing on father's rights, and this even applies in cases that have involved proven domestic violence.
I note that someone has said residence was shared up until the final order was made giving the father custody; an important question that should be asked... was shared residence ordered by the court, or did the mother agree to this? Children are currently being split down the middle 50/50 as if they are property, and mothers who have carried their children and bonded with them from the moment they were conceived, are now being cruelly seperated from their children, to appease fathers rights groups. This is no longer about ensuring father's having contact with their children, it is about children being regarded as property, and I think this is very sad.
With regards to false allegations, I believe polyograph testing should be brought into play. The mother's allegations may not have been false, but the courts rely on evidence, and if there is none, then any such person who braves making such allegations is on dangerous ground. Because potentially the tables can be turned on them, to suggest they are obstructing contact for no good reason. If this is the case here, I feel truly sorry for the mother.