If I apply for a job directly from a company and then a head hunter reaches out about the same job?

I applied to a job on a company website, then a head hunter reached out to me about a job opportunity that happened to be the same job I had already applied to and told me about it as well as the comp range. I reached out to the head hunter and they had told me they had not hear back, but i received an interview from the company which makes me think its from the direct application.

My question is, if the HH said the compensation range is $100-$110k, should I expect it to be higher with a direct application because there will be no fee? Can i leverage that info to make more than what the recruiter said the range is?