Adjusters assigned to investigate your claims will conduct interviews and they routinely look for discrepancies in the transcript of your initial reporting. Regardless of what a call center operator or insurance adjuster promises, if discrepancies are alleged they will refuse a copy of your statements under the guise of protected work product. New York court opinions are clear on the matter, in that, business records must meet specific legal criteria to be deemed protected work product, however, the cost to get your own ruling can be cost-prohibitive. Your best bet is to obtain professional representation, especially if you have a large claim.
Also, See; More On Recorded Statements And Who Is Considered A Suspect