(a) That's right. A will be allowed to lead evidence of what was agreed orally, to show that what was recorded in the written contract was not what the parties had actually agreed. In such circumstances, the court will rectify the written contract, and substitute the terms actually agreed.
Such cases are an exception to the parol evidence rule because the presumption against other (or different) oral terms is easily rebutted when there is an error recording the agreed terms. But before a court will rectify a written contract, the terms to be substituted must be precise, certain and clearly agreed.