(b) That's wrong. Because the parol evidence rule can have unfortunate results in cases like this, the courts have sometimes responded by saying: 'Even if there are no other terms in the written contract, we recognise the existence of a separate contract, which exists alongside the main contract.' This separate contract contains the additional orally agreed terms.
The separate contract is called a 'collateral contract' or 'collateral warranty'. It may be difficult to establish a collateral contract. All the ordinary requirements of contractual formation must be satisfied in relation to the collateral contract, namely, agreement on sufficiently certain terms, the intention to be contractually bound by the promises, and the exchange of consideration.
It is likely that a collateral contract exists in the circumstances outlined in the example.
Note: The consideration given in exchange for the promises contained in the collateral agreement is the agreement of the other party to enter the main contract.