This happened to me once at Las Vegas. The kiosk said something about it being too late to check in for this flight. However, the helpful agent immediately produced my boarding passes. She told me that the computer doesn't know that the flight is half empty and that there are very few people at security. She said, "Go straight through security to the gate. Don't delay." I easily made the plane.
Still, I show up much earlier now. I don't want this kind of avoidable risk.