I can tell you that having dealt with headhunters from both sides, as an employee, and as the person doing the hiring, I hate the bad ones no less regardless of my current role. I have quit good jobs because the contracting company I was working through were being jackasses. I hated to do it, but it had to be done.
The problem from the interviewers side is, even if they like you, you've pointed out that the contracting company misrepresented you to them. That means that the contracting company is disreputable, and they likely won't want to do business with them anymore. If they hire you, they have to continue to do business with them, and deal with potential issues that will arise between them and the contracting company, and you and the contracting company. Unfortunately, they typically can't just circumvent the contracting company at this stage, so you might not get the job, simply because they don't like the contracting company.
The two of you get hired or passed up as a team, so you need to work as a team. They need to understand that if they place you somewhere you're not happy, it won't last, so they're better off putting you somewhere you're going to be happy, and to do that, it involves working together and not lying about things to either side. As a side note, I tell every headhunter before they submit me to any job that they are not permitted to change my resume in any way. I've never had them say no to that request, however, they have gone ahead and changed it once, in which case I informed them I was no longer interested in the position.
Contracting companies/headhunters work for you, which you seem to get, now the second part you need to get is that there's a million of them out there, and they're all fighting over you and the positions, they aren't in a position to pull that kind of crap, and you should be sure to let them know.