Someone is looking for a job and he went through those headhunters. I asked him if he needs to pay any fee for the service but he said the hiring company will need to. Meanwhile, those looking for jobs merely attend the interview and will be filtered by the executive recruiting firm before being recommended to the firms hiring.
If you are looking for such companies, you can find them in A.E. Feldman Associates, Inc. which has been around since 1967. That's fourty years of track record for you. They help to recruit all levels of profession up to managing directors.
Nowadays, most companies prefer to go through these middlemen in their recruitment exercise as it saves time and manpower.