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R1 gets 2B. You've quoted the rule yourself.
The rule is two-fold:
1. Award what you think the runner would have gotten.
2. If that award doesn't give the runner one base beyond his last-aquired base, give him one base.
Basically, OBS penalizes the defense everytime. In OBR, R1 would be allowed to remain on 1B (no award). However, Fed wants to prevent F3 from trying this on every play, so they give the runner the next base.
Edit: The rule allows the umpires to award more than one base. For example, speed-demon R1 with a base hit to the RF corner. You know that he'll make it home easily, as defense was shifted to LF. After rounds 2B, he's obstructed by F6. You can award R1 home on the play.
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