Sorry to hear you were delayed - hopefully you were accommodated on another flight quickly.

I've always thought that was the standard rule: Be there at the scheduled departure time as things can change. A delayed flight can have its delay eliminated for a number of reasons (if weather clears, a mechanical issue gets resolved quicker than expected, etc.).

From the US Website:

If you are not checked in and waiting in the boarding area at least 15 minutes before the scheduled departure time for domestic U.S. (30 minutes for international travel), your reservation may be canceled and you will not be eligible for denied boarding compensation.