The award is based on umpire judgment, as it must nullify the act of OBS. Without video, we cannot legitimately comment on the correctness of the judgment call in a particular case.
As a general rule, if a runner is tagged out on a close play after having been obstructed, he probably should have been awarded that base, all else being equal.
If the awarded base is 2B and the runner advances beyond that base, he advances at his own risk. Any outs made at bases beyond (or even back into) the awarded base will stand.