If System 7 had been on the market for 2 years by the time the LCIII was released, then it's not surprising that you can't run System 6 on it. You can't downgrade a system to a version that was released prior to the version that the machine shipped with. It's Apple's way of keeping the user experience as current as possible. They can't force you to upgrade, but they can prevent you from downgrading. They've always done it that way.