I do not think this is accurate. There is no language that reflects this on Delta's website. Let's say you're a 360 flying from Vegas to LAX and you get upgraded at the gate, I don't see anything that prevents you from accessing the lounge at LAX when you arrive. Another example would be if you're upgraded at the gate at JFK and then your flight is delayed several hours. I do not see why you wouldn't be able to access the Delta One Lounge while you wait for your delayed flight.