OK, so you'd rather work for a guy who fires the adulterer the next day, not the same day that he finds out he's been poking his wife? Because he's taken 24 hours to "think it over"?
I can understand if the employee was caught stealing petty cash or fudging the time sheets; then you'd want some semblance of due process to gain absolute proof, give him a chance to resign rather than be fired, etc.
It's not about the proof required to fire him. It's about understanding the situation entirely before reacting. Immediate reactions are usually problematic because emotions are involved, particularly in this case.