Can an insurance company compel a policyholder to use a particular repair facility?

No. Any insurance company attempting to do so would find itself in direct violation of Section 2610 of the New York Insurance Code [N.Y. Ins. L. Section 2610 (McKinney 1997)]. It would then not only be subject to severe penalties from the Insurance Department, but it would expose itself to a civil suit by the policyholder for unfair and fraudulent trade practices.

*New York Insurance Law Section 2610*
Whenever a motor vehicle collision or comprehensive loss shall have been suffered by an insured, no insurer providing collision or comprehensive coverage therefore shall require that repairs be made to such vehicle in a particular place or shop or by a particular concern