Is it a balk?

[Don Mueller]

Hitters get 'game winning RBIs', Fielders routinely get credited with 'game saving catches' a reliever comes in at the bottom of the ninth with 2 outs pitches to one batter and gets a 'save'. These are all one play or one batter episodes
Why is it so outlandish to suggest that an umpire who screws the pooch on a rules interp which definitively results in a score can't have some responsibility in the outcome?

If, instead of a balk, the batter hits a single and scores R3 everyone will look to that play as the game winning hit. If the ump blows a rules interp that results in the same run scoring we're not to think it has any bearing on the game?
If the ump makes any judgement call that results in a run, good bad or indifferent from the perspectives of any onlooker, player or coach I would never credit the ump with any responsibility for the outcome, but a blown rules interp is different.
Which is exactly why there's a thing called a protest.
The fact that there is a provision for protests acknowledges that a blown rules interp can effect outcomes.

Which is exacly why as umpires we need to know our rules!