What does the service agreement say as to the service provider's responsibilities?
Right or wrong, the employer has made the decision that this is no longer an employee, which has created a severance from employment. The service provider should caution the employer about the possible ramifications if there is a determination that a severance of employment did not actually take place, and should recommend that the employer seek a legal opinion.
Beyond that, I don't think the service provider owes a duty to investigate the employer-employee relationship.