They are trusting you now?!? It's an affidavit! You lie, you're out of there! My only issue is the presumption of guilt to disqualify seems more important in the process than what the Constitution and the US Justice system mandates.
I am running out of fingers and toes counting all the people who's lives and careers are ruined each year by accusations without adjudication. It's part and parcel the same thing!
Yes, it is trust. If you sign an affidavit and LSP doesn't check to see if you are lying, it's LSP trusting you are being honest. If LSP is going to not trust you and check to make sure you are being honest, they will have to research every entry without either a disposition or submitted documentation.
So here's a scenario. John walks into LSP to get a permit. He hands over his DL to show his identity and signs an affidavit indication he had no disqualifying convictions. LSP pulls his DL photo from the DMV database and prints his permit. He's out the door with his permit in 15 minutes with no background check being conducted. Do you feel that process is how things should be?