Former agent hat on. Every time a gate change is made numerous terminal-wise announcements are made. Local ops does everything possible to keep gate changes nearby the orig gate, but this isn't always possible. Late gate changes (i.e. within an hour of departure) usually lead to delays. There were likely many other pax who weren't yet at the gate who somehow found out about the change. If the monitors were in fact wrong (that's what camera phones are for), that's on DL, but the greater responsibility is on the pax in this case. DL has a 15-minute no show rule. Showing up at D-15, means you were at risk of being "15-minute ruled" anyway. Even if the 15 minute rule weren't there, showing up at D-15 doesn't leave you any wiggle room.
https://www.delta.com/us/en/check-in...estic-check-in
Just out of curiosity what flight were you scheduled on?