Spectator interference is actually pretty rare. It does not mean it does not happen. Here is a play from the other night:
Rule 6.01(e) (3.16 in old format) covers this.
When there is spectator interference with any thrown or batted ball, the ball shall be dead at the moment of interference and the umpire shall impose such penalties as in his opinion will nullify the act of interference.
APPROVED RULING: If spectator interference clearly prevents a fielder from catching a fly ball, the umpire shall declare the batter out.
The distinction on this play is where the fielder is at. If the fielder goes into the stands, he is fair game. If the fan comes over the field, it is interference.
Although neither the outfielder nor ball was not touched, it does look like the OF was hindered so the out was called. I agree with the call. I think if it is close, the benefit of the doubt has to go to the defense. Otherwise, fans would be leaning over the field all the time.
Spectator interference is covered on page 65 of RuleGraphics