How is PayPass/payWave secure when PIN is required after presenting the card to the contactless terminal?

The popular claim is that a chip-and-PIN payment card is more secure than a card with magnetic strip because the card data is hidden deep inside the chip and the ATM or POS terminal sends the entered PIN into the card for confirmation (or rejection) instead of reading the correct PIN from the card and comparing it with what the user entered. So as the data is not exposed it cannot be copied and this prevents various fraud scenarios.

Now meet PayPass/payWave contactless payment technology which is now embedded into numerous new chip-and-PIN cards. You can briefly touch the terminal with such a card and the field of the terminal induces current in the card circuitry, the card turns on and runs an encrypted radio exchange with the terminal - all in fractions of second. That's all it takes if the purchase sum is small enough (which means under USD 30 in most cases). No problem - the encrypted radio protocol still allows the "is this one correct" validation style exchange.

What happens if the purchase is not "small enough"? Here's a promotional YouTube video that shows what happens. The buyer touches the terminal with his card and takes the card away. The terminal prompts for the PIN. The buyer enters the PIN and the terminal somehow validates it.

How is the PIN validation secure in the scenario when the PIN is being entered when the card is no longer connected to the terminal?

Okay, it could have obtained the PIN from the card when the card was close to the terminal and compare it after the buyer entered his version. But it implies that the card gives the PIN away instead of doing the "is this PIN correct" style validation inside its chip.