I mean, either way you've killed at least one cop which means life in prison or the death penalty.
Plus, I'm pretty sure that he/she did shoot the deputy.
If my friends and I had heard a rumor that one of our friends had shot the deputy we wouldn't know what to think at first. But if he or she came in and just said "Hey, I didn't shoot the deputy" and then changed the subject, we'd give them the benefit of the doubt.
But, if every 30 seconds they kept saying over and over again that they didn't shoot the deputy, we'd figure they had a guilty conscious and wonder if not only did they shoot the sheriff and the deputy, but perhaps the dispatcher as well.