INS will not do nothing
INS is not in charge of medical license and has no authority over individual practitioner. But complains through New York Medical Board will work!
Medical Board is the only one oversee docter's medical practice. They has the right of revoking license based on professional misconduct, including "failure to produce medical record" (sounds simple, but so easy to attack).
Remember that the infamous Chicago ganster Al Capone was not indited for murder, but was indited for tax evasion.