(b) No, the best answer in these circumstances is probably yes. Compare this example with the previous one. The difference lies in whether the court thinks the parties intended the written contract to be the complete agreement. If what was agreed orally is of great importance in the circumstances, or the sort of term that would usually be found in that type of agreement, the court may conclude that the oral undertaking was intended to be a part of the contract. This rebuts the presumption (on which the parol evidence rule is based) that the written contract is the complete agreement. Once the presumption is displaced, evidence of the oral term is admissible.
You may sometimes find it hard to distinguish the cases on their facts, but it will help to remember that the courts are concerned to do justice, not just to apply rules mechanically.