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The rules of civil procedure do not apply. It is the common-law of contracts. If you can tell me what state are you in, then perhaps I can find some case-law for you. However, please note that it is the application of general principles of contract law that govern here. In addition, there is no case law on point with how a statement can be retracted. Once a statement is given, it is then floating around in the ether. It can be explained by later statements, affidavits or testimony.
Yes, your best bet would be that there was no mutual assent (meeting of the minds) since party was falsely induced to believe that party B was performing a service for his/her benefit, and later learned that party B had someone else perform the work. The statement cannot be disqualified. Party A can provide a latter statement or affidavit explaining why he/she made the first statement and why the first statement is incorrect.