Like he has to provide forensic level testimony with a timeline of who's holding a child while it's dying?
That's some psychopathic level lack of empathy for someone who's child died.
Fabricating a story about his child to win points seems directly relevant here.
You can simultaneously have empathy for someone for the simple fact that their child died, and also think they're lying about the details for their own personal gain. The two are not mutually exclusive.