While what you said is true, this case is rather different from your regular cases.

The killer was already prepared to face the law when he killed Abe for personal vengeance, not against Abe but the Unification Church. Killing Abe would send a strong message to not just the church, but more importantly to the public. But if he doesn’t admit his crimes, then there would be no message; he has to use his background for the message to come through. And he’s been pretty successful. Attention and criticism of the Unification Church intensified and there are now more people who call it as a cult, and politicians have distanced themselves from the church as well.

People see Japans conviction rate and think "that's amazing" before thinking about what would be required to be correct that consistently.