If the stats are published or not, parents and coaches already question scoring decisions. I still officiate games, and at the younger age groups I get questioned more about awarding secondary assists than I do about getting calls right in a lot of games. As far as shots goes, that has always been arbitrary even at the NHL level (I can remember the stories about the way NJ was legendary for some of the shot totals they came up with in the 2000's), so that will never be agreed upon.
I disagree with the idea of giving out awards for scoring accomplishments because we already see players (and parents) who are ONLY concerned with how many goals their little player scores and that would only perpetuate selfish play. The bare minimum should be that the stats should be published and updated each week during the season. At the very least, this would provide a single source regardless if people are satisfied with the accuracy. People aren't always happy with the accuracy of the stats the NHL publishes, that's the cost of doing business.