Interesting... after checking the rulebook, this is apparently how it's scored:
If R1 gets in a rundown and makes it safely to 2nd (with no errors) or safely back to 1st, then R3 gets credit for a stolen base.
But if R1 is out in his attempt to steal 2nd, then R3 doesn't get credit for a stolen base.
So in the case referred to here, R3 would not get an SB.
Here's the wording from OBR:
10.08(c) When a runner, attempting to steal, or after being picked off base, evades being put out in a run down play and advances to the next base without the aid of an error, credit the runner with a stolen base. If another runner also advances on the play, credit both runners with stolen bases.
If a runner advances while another runner, attempting to steal, evades being put out in a run down play and returns safely, without the aid of an error, to the base he originally occupied, credit a stolen base to the runner who advances.
(d) When a double or triple steal is attempted and one runner is thrown out before reaching and holding the base he is attempting to steal, no other runner shall be credited with a stolen base.