Recruiter $$ Offer by Coincidence Matches Your Previous Wage

How many of you have experienced this scenario?: A recruiter has a job you might be interested in. He/she asks you to fill out a form and asked how much you were making at your previous job. Like a fool, I told the truth. Two times in the past week, a recruiter has told me that my previous wage just happens to be the same as the job they have on the table. Coincidence? Or is this a common tactic headhunters use to make more profit at your expense? Have you or would you lie and jack up your wage history?

Another question: I found the name of the company that has the job the recruiter is telling me about. Should I try to bypass the recruiter and apply directly? Would there be any consequences in doing this?