It's been a few years, but my last experience in contracting like this was that the recruiter MADE themselves non-optional. In order to access the recruitment service (primarily to reduce the time invested in screening applicants), companies have to agree to make the payments to the recruiter. Advertisements for positions are made by the recruiter and don't include details of who the actual company is, until after you're under contract.
Additionally, companies and contractors are in breach of contract if they tell each other what they are paying/being paid by the recruiter. My last employer "accidentally" let me find out this information, and suffice to say the recruiter was making a very nice profit. AND you're required to not work for the employer directly for a period of time after the contract ends.