Game Theory Auction

I was reading an article about economics and game theory and came across the following paragraph:
"I happened to walk into a lecture on game theory, and the lecturer gave an example of a beautiful model called a second-price auction," she says. "In a second-price auction, all bidders are told: Bid in a sealed envelope the maximum price you are willing to pay, and in fact you will pay the second highest price offered. That way, they have nothing to lose by offering the true value. Let's say they bid 100 and the second price was 80, then they will only pay 80 and benefit from the difference anyway. If they bid less than the second price, they will lose the product. Therefore, it is better for them to bid the price that the product is really worth to them. Studies show that this is a method that encourages people to tell the truth."
I think it doesn't necessarily incentivize people to bid the price that the product is worth to them, because if it's important to them to buy the product then they won't want to risk bidding lower than the second place. Maybe two people will bid above their price and they'll win the auction?
Am I missing something? Can you help me understand?