A psychiatric defense is an affirmative defense. There's lots of affirmative defenses for different reasons, but the main point of an affirmative defense is that you're saying you did do it, but aren't guilty because of X. Its essentially pleading guilty. The prosecutors job is then not to prove you did it, but that you aren't crazy/acting in self defense/were entrapped, etc. The prosecutor was probably sitting happy not doing much thinking it'll be an easy case to prove the person was of sound mind. Now they have to go back to rebuilding the case from the evidence that was legally submitted. Prove where he was at what time for weeks leading up to it, where he got everything, where he went after and how. It's a shit load of work.

But Luigi was at my buddies house in Utah when it happened so there's no way he could have done it. They need to prove beyond a reasonable doubt that he wasn't there.