What is really puzzling about that is Brad submits to the examination, but then consents to a temporary custody order in favor of the Rentz' before he is arrested. It appears his lawyers expected him to hold up to examination, but then when they saw what he said, they realized their mistake and buried the issue as quick as they could. This would suggest Brad was not forthright with his attorneys at the beginning, or that Brad actually convinced them he could get through the examination unscathed. Had he told them he did it, they would have circled the wagons and their client would have been in a better position going into the criminal trial. Maybe they thought he also wouldn't be charged. In any event, allowing him to participate in the examination --regardless-- of innocence or guilt was a major mistake.
From a public perception point of view, Brad could have released a statement "I love my children more than life itself, and to protect my ability to be there for them in the future, my attorneys have prohibited me from testifying in the custody case at this time. There will be a time I will testify to win custody, but it is in their best interests that I not do that now. I wish the best for my children in the capable and loving care of the Rentz family."
I suppose hindsight is 20/20 for Brad's team, but submitting to that deposition was an obvious mistake even at the time.