Fly ball catch with a runner on first

Question
I was hoping someone could shed some light on this scenario.  

Base runner is at first base the batter hits a line drive to third base the base runner is now running back to first base at the time of the throw.  The ball is thrown out of play on the throw back to first base in an attempt to catch the runner and the time the player is still giong back to first base to tagup and avoid the double play.  Should this player get 2nd or 3rd base?  Because they were heading back to the bag I would assume that they should only get 2nd base but the few times it has happened the player was awarded 3rd base.  Which rule is correct and why?

Answer
Robert,

It is correct to award the runner third base. However, the runner must touch first before advancing to second or he could be called out on an appeal.

Here is the applicable comment from the Official Baseball Rules. The section detailing your question is in the second paragraph:

Rule 7.05(i) Comment: The fact a runner is awarded a base or bases without liability to be put out does not relieve him of the responsibility to touch the base he is awarded and all intervening bases. For example: batter hits a ground ball which an infielder throws into the stands but the batter-runner missed first base. He may be called out on appeal for missing first base after the ball is put in play even though he was 揳warded?second base.

If a runner is forced to return to a base after a catch, he must retouch his original base even though, because of some ground rule or other rule, he is awarded additional bases. He may retouch while the ball is dead and the award is then made from his original base.