Might this just be the parents responding to the stimuli of each others presence? E.g let me think about whether or not he/she will pick them up or should I do it. It makes sense that both parents would think this. In the situation where they are alone, such a computation does not need to be done by the brain.

There is no way to actually characterize the thought processes using these imaging methods. No where does this implicate that the actual actions or thoughts specifically relating to the child are any different. This makes the conclusion much less interesting.