So if he does want to stay with his gf, feels horrible about it, won't be repeating the mistake, you still think he should be admitting that he cheated? I just don't see how that is a smart thing to do. Better to live in "cautious optimism" (as the above poster said) and live with his guilt. Use it to not repeat the offence.
Though I definitely consider the STD angle a valid one. If there was no condom usage in the incident then he has to admit it, can't be irresponsible when infectious disease is involved.