At least in Major League Baseball, the umpire's call could be partially correct, depending on their interpretation of what occurred.
In the Major League Baseball Rulebook, 6.01(a)(5):
It is interference by a batter or a runner when:
- Any batter or runner who has just been put out, or any runner who has just scored, hinders or impedes any following play being made on a runner. Such runner shall be declared out for the interference of his teammate (see Rule 6.01(j))
This would depend on the umpire ruling that the action of the runner impeded a play being made on another runner. This is impossible to tell from the scenario above. If this was a situation where a runner was alone on third, and the runner scored roughly simultaneously with the batter-runner reaching first base, and the batter-runner did not round first base (so trailed off to the dugout side of the bag), then likely there was no play to be made, and no interference call should be made.
However, if there are other runners on the basepaths, or if there was any potential at all for a play at first, or at any other bag, or if the batter-runner rounded first towards second (even if he did not advance), it's likely the interference call was appropriate. In that sort of situation, the umpire is going to tend to give the benefit of the doubt to the fielders.
I don't see any reason the run should not score, though, in either case. The umpire has vast discretion, if they feel something that is not covered in the rules occurs - 8.01(c):
Each umpire has authority to rule on any point not specifically covered in these rules.
However, I don't see how this would apply; but again, it's hard to say without being at the game.