It depends, but mostly I agree with you. If you are a rare talent in the market or you have several pending offers, they will really make efforts to accommodate your needs. They tend to think working with you can help them make a good deal with the employer faster. On the other hand, I think you know it, Headhunters never work for candidates. Instead, they are hired by your prospective employer, so in principle, they are helping the employers, not candidates.
My experience is positive.But I feel that it's much harder to negotiate salary if the job is introduced via a headhunter. I guess it might be due to the reason that the employer has to pay for a high commission fee to the headhunter.