Can I stop working with a headhunter, but still interview at the firm they introduced me at?

I'm working with a few headhunters for quant positions. I'm pretty frustrated with one of them, and I no longer want to work with this person. If I stop working with them, is it still possible to interview at the firm they introduced me at?

Story:

This person asks me the same question repeatedly multiple times a week. They've also been trying to rush me to interview for this paticularly position ASAP, claiming how there's only a single position available, and that they have X number of candidates in the final round already. I mean I spoke with the hiring manager who told me this isn't true. When I told the headhunter what the hiring manager told me, the headhunter insinuated that the hiring manager is wrong and that there is indeed one position available. I seriously feel like I'm dealing with a poor man's car salesman here, and I no longer want to work through them.

This isn't just a one time occurrence. This has happened 5+ times by email and phone in only the past 10 days.