The parol evidence rule of itself is never an obstacle to reformation, provided there is satisfactory evidence of a mistake in integration. If the parties intend to express the terms of a transaction in a writing, which is then to be looked to as the sole repository of those terms, the longstanding tradition of the law courts, described as the parol evidence rule, has been that the writing is controlling. If through mistake the writing failed to express correctly what the parties meant to express, the law courts still regarded the written word as decisive, but it has been recognized for a long time that equity will give relief through correction of the writing. Certainly by 1801, if not earlier, it was settled in English law that the parol evidence rule did not bar reformation in equity. Nonetheless, there remains a certain amount of confusion due to the occasional failure to distinguish between the parol evidence rule and the statute of frauds. There are cases refusing reformation through the use of "parol evidence" which might be thought to rest on an application of the parol evidence rule when in fact the reason for denying relief was the statute of frauds.
George E. Palmer,
Reformation and the Parol Evidence Rule,
Mich. L. Rev.
Available at: https://repository.law.umich.edu/mlr/vol65/iss5/2