Strange situation, injured runner

[Jay R]

Situation tonight that had the crew talking after the game.

R1, nobody out. Batter hits a drive in the gap, R1 falls after rounding 2nd base and is injured. BR goes for a double and slides into 2nd base is safely. F4then walks over to R1 and tags him out as he has still not moved since falling (R1 was about 15 feet passed second base). After the injured player is removed, we continue the game and nobody says a thing.

After the game, myself and the two other umpires discuss the play. Was the BR entitled to 2nd base if R1 had not yet touched 3rd base. In other words, when the BR was tagged while already on 2nd base, should he have been out? My partners thought he should, I couldn't understand why he should be out.

BTW OBR rules, if that makes any difference.