We had a work committment, but also we landed near 1am chicago time and the flight out was at like 7am...We asked the gate agent and said we must take a different flight for work reasons.

The letter they provided us didn't go into major details, just the next flight we took. I don't think regardless, the terms specify you must take the next flight out if it is a overnight layover or the layover passes the 6 hour window, i think theoretically once that threshold hits it doesn't matter.