I was under the impression that the card created a cryptographic signature on the transaction, and the card had to receive the correct pin before it would sign

I was under the impression that the card created a cryptographic signature on the transaction, and the card had to receive the correct pin before it would sign it. Which is why you have to leave the card in the reader until the total is completed. Is this really not the case? Or does the card still cryptographically sign the transaction, but doesn't process the PIN first (other than answering valid/invalid)?