(b) That's right. You might think that there is no good reason to stop B giving evidence of what was said during negotiations (and calling a witness if she has one) but the court would probably not allow it. Why? Because when a written contract appears on its face to be a complete agreement, the courts will presume that the parties intended it to contain all the agreed terms. Therefore, further evidence of additional oral terms won't be allowed. This is the 'parol' (or oral) evidence rule. The rule forbids leading evidence of orally agreed terms when the contract in question is recorded in writing and appears complete.
The benefit of the parol evidence rule is that it gives certainty as to the agreed terms when contracts appear to be completely expressed in writing.
In the present example, although the written contract does not contain every possible term that might be included in such contracts, enough terms are recorded to appear to be a complete and workable agreement. That is normally enough to bring the parol evidence rule into operation.