Funny thing about this is that there is a whole section of the Rule Book dedicated to scoring a baseball game. It is far and away the largest section of the Rule Book. Rule 10.04 defines RBI's and this specific scenario is addressed in 10.04(a).
More people than you think have no idea it is there. I think many believe this is one of those things that is kind of made up and really can be flexible. No - there are definitions the same as there is for determining the size of the field or strike zone.
Ironically, It is the only section not read by Umpires. FWIW - There is a section in the Rule Book defining their role too it is Rule 9. Almost no one is aware of that except the men in Blue themselves.