For the games that get to late-game, the ADC probably has on average the most input in late-game fights. But a lot of games don't get past 25 minutes with scores close enough that whatever the ADC does matters at all--often due to the Mid or Jungle of one team snowballing hard. And how well ADCs do late has a lot to do with how well the supports set them up for success. I've had 0/6 adc games followed by 12/2 games where I played about the same, but had very different quality supports. Sure, it looks like I carried if I'm 12/2, but often it's just a Pro Thresh or Nami who can't seem to miss skillshots. And certainly during laning, I'm much more concerned by an enemy support than I am the enemy adc.
"Carry" does imply that one member started snowballing, but the reasons they did don't always have a lot to do with their own play.