They aren't getting a benefit. The ball is live and they have to hunt the ball down and make a play. Also, the penalty of throwing the ball away is that the batter who would've been out already got a base. Going from there is a risk to both teams. Proceed at your own discretion.
Would you also like the runners who take off on a steal to be able to stop if they don't get the right jump and go back to the base without risk of being thrown out?
But they are getting a benefit. The reason the runner is on first is because the ball was thrown away. And he's still on first base. By marginally shifting his shoulders towards second base doesn't put him on second base.
It's not like he was caught in a rundown.