NFHS Interp on OBS award to other runner

[CecilOne]

Another NFHS Interp.

SITUATION 16: R1 is on second base and B3 is at bat with one out. B3 hits a sharp grounder to F6, who bobbles the ball as B3 rounds first base, is obstructed by F3 and stumbles. Seeing the ball in front of her, R1 freezes at second base. Before B3 can get back to first base, F6 throws the ball to first base to get B3 in a rundown. To complicate things further, during the rundown, B3 is obstructed again. B3 slides into second base and is tagged out on a close play. In (a), R1 advances to third base, and in (b), R1 stays at second base, seeming somewhat confused. RULING: In (a) and (b), the umpire should call obstruction the moment it occurred and signal a delayed dead ball. When B3 was tagged out, the umpire should call time and award B3 second base. In (a), R1’s advancement to third is legal. In (b), the umpire would award B3 second base and R1 third base. (8-4-3 Pen.1)

Why is R1 awarded 3rd? Is it because B3 must be given 2nd?
Does that mean you have to assume that the rundown would not have occurred w/o the OBS and therefore, B3 only tried to advance to 2nd because of the OBS preventing a return to 1st? Or is it because the second OBS impeded B3 from 2nd, which the case does not say?