I've never cared for a lawn in my life, so purely out of curiosity, why should a sprinkler system be on in the early morning? Wouldn't morning dew take care of watering grass around those hours?
As for why it's not "ideal" to run sprinklers in the middle of the day, the idea is that if you water early in the morning, then all of your sunlight hours beat on watered grass. If you just started watering in the afternoon, your grass has already been in prime morning sunlight without the watered soil to boost growing. It's not necessarily bad, it's just not ideal.