The issue was not whether Sweeney ran into the kicker. He got the holder, too. Go to the 31 minute mark of this documentary:
the issues were purely about interpretation of the rules. The refs ruled that the game cannot end on a penalty against the defense and marched off 15 yards , giving Notre Dame an extra play which they used to kick the game-winning field goal. Syracuse pointed out that the rules also said that once a ball is kicked, the kicking team becomes the defense team: Syracuse was the offensive team at the point Sweeney made contact. the NCAA agreed but also said that that rule #1 was that the score at the end of the game was the final core of the game, meaning that even if an error was acknowledged after the game had ended the NCAA could do nothing to change the final score. Syracuse pointed out that, under the rules, the game ended with the unsuccessful kick, since we were the offensive team at the point of the infraction. The NCAA said they could do nothing and that Syracuse's only recourse was to ask Notre Dame to concede the game, as Cornell had famously conceded the 5th down game to Dartmouth in 1940:
Fifth Down Game (1940) - Wikipedia
Notre Dame refused to concede and most of the country supported them, as there was no question the foul had been committed. This prompted the reference President Kennedy made in the speech shown in the documentary. The rule was changed the next year so that the kicking team didn't automatically become the defense in the instant of a placekick.