Can SEO companies really have special relationships with the search engines like some of them claim?

A company called me and said they have a special relationship with the search engines, and they will place my site in the first position at all of them for X amount of money. Can they really do this and should I consider learning more about it?

Most likely this company is simply buying the sponsored PPC ad spots and will then resell them to you with a high markup. Nobody has a “special relationship” with Google, and you can’t buy your way to the top of the natural results.