clock mismanagement at end of game

[mhmob]

hi there- new to the forum, long time bball player/parent/junkie. had an issue at our league that abides by NJ HS rules. ball inbounded with 3.9 secs left, winning basket scored with .1 sec left in game. scorer's table then admits to refs that they started the clock late and game shouldve been over before shot went up. Is this the breaks of the game or do officials have some authority to overrule? of course, my team was on losing end, but only the 1st game of a season so no problem.(had the moral victory of feeling like we played well as a team, right?)
thanks for any input!