It is slightly more complex than that. EMV is designed as to allow configurable methods of card holder verification and to be backward compatible with back-end systems. This means that PIN is not required to unlock card and even not mandatory for successful transaction. This is configurable and whether PIN is actually required depends on both card's and terminal's configuration and current state, this allows for things like small payments without PIN (which is how NFC cards usually work).

Because of backward compatibility, the transaction signature generated by the card has to fit into 8 BCD digits, which essentially precludes use of any kind of public key cryptography. Actual algorithm for how signatures are generated and verified is issuer defined and only card issuer can actually verify signatures (terminal just blindly trusts whatever was returned by card).

Public key cryptography (ie. RSA) is used in EMV to verify that card was really issued by claimed issuer (card contains data structure that is signed by issuer's key) and to optionally encrypt PIN sent to card for offline verification (PIN is somehow regarded as super-sensitive by banking industry)

One can certainly imagine better design than EMV (eg. without various implicit trust relationships), but in all, it is pretty reasonable mechanism nonetheless.