Should Payton have challenged the Bush fumble?

I think the non challenge on the Miller fumble influenced the challenge on the Bush fumble. The coaches in the box have the game feed on TV and they saw what we saw well before Pitt snapped the ball. I thought it was probably to early in the game for Payton to risk the challenge.

Maybe Payton needs to reward players for letting him know if he should challenge on a play and penalize them if he challenges their play and don't get the reversal. The players know when they fumble or make a catch but their competiveness skews their honesty many times.