Many third-party recruiters are simply matchmakers, not retained agents of a company. Sure, they still get paid by the companies for matching employees, but their motivation is still to make matches, not get either the employer or the employee the best deal.

> fiduciary duty

I think you are misusing that word. A third-party recruiter does not have a fiduciary duty to the company with the role unless they have been empowered to make the hiring decision themselves. I don't know of any agencies with such power.