RBI book scoring question

[Rennikselum]

Can a run be scored without someone getting credit for the rbi?

We play NFHS rules. Nobody on base. No outs in the inning, batter hits a triple. Throwing error allows batter/runner to score on the play. Does the batter get credit for an rbi even though the run was on an error?
In the rule book I can only find-
Rule 9-3 Art 5
"a rbi is credited to the batter when a runner scores because of the following:"
e.
"an error,provided two are not yet out and the error is such that the runner on third would have scored even if there had been no error."

Thanks

 

[fastpitch]

Short answer is yes. There can be a run scored without an RBI.

Based on the definition you provide... if the run wouldn't have scored without an error there would be no RBI.

 

[bosoxfan]

There are a bunch of times that runs can score without an RBI. passed balls, double plays

The rule you are talking about would be for example with less than 2 outs and a runners on 3rd, ground ball to the second baseman runner on third braeks for home 2nd base throws it over the first basemans head. she reaches on an error but gets credit for the RBI the same as if she were thrown out