What part of this are you not understanding? Highest bid wins. Sniping doesn't change that. If an auction is at $20, and you put in a max bid of $40, and then I snipe with $35, you still win.
The only overall affect sniping has on prices is maybe keeping them lower by reducing the possibility of "gotta have it" bidding wars.
In my last example, suppose my max bid is $45. I snipe the auction at the last second and beat your $40 max bid to win. What's the issue? If I'd put that bid an hour earlier, you might have gone in and put in a $50 max bid, even though you already told yourself $40 was your max bid. It's stupid! But everyone does it. Sniping avoids that completely.
Make sense?