The distinction is - if there's one person with the authority to say yes to your salary requirements, and three people who only have the authority to say no, does it benefit you to go via those three people?
In some organisations it might benefit you! If your salary needs to be approved by a hierarch of the fourth level but you'll be reporting to a hierarch of the second level who'll be benefiting from your genius, they might be a highly motivated advocate in your favour.
In other organisations though, the more opportunities there are to say no, the higher chance of the answer being no.
Sometimes, it's the manager because they benefit the most from hiring you and the organization probably values their opinion, but some managers are pushovers with zero people skills and will be useless.
Sometimes, it's the recruiter because they are the most experienced with the hiring process and know what wheels to grease; sometimes they're useless because recruiters are often viewed as interchangeable cogs.