The difficulty is that the family court is a lot less strict about evidence and rules that other courts.
Obviously the overriding interests of the child are the priority, not necessarily following rules to the letter. This is very frustrating if you are a party that complies with the rules and the other side does not.
However, in this case, where the court has been very clear about the filing of evidence in the run up to a hearing, then parties should need to see permission to submit additional evidence if they intend to or the whole thing is in danger of spiralling out of control in terms of the timetable. Additional evidence needs responding to properly and as such late filing nearly always ends up in adjournments, which the court is against unless absolutely necessary. Quite of too, parties file additional 'evidence' thinking they are helping their case when in fact they have missed the point entirely - the objective is not to throw mud at the other party but to find the best outcome for the child.
Really the only justification for an additional statement would be if there had been an event of significant importance in the intervening period between the final statement being filed as per the timetable and the hearing itself. But, as I said, the court can sometimes be flexible around there issues and there is no hard and fast rule as ultimately it's down to judicial discretion.
Additional statements from third parties should not however be allowed in at the last minute.
I hope that this clarifies things?