If a third party recruiter doesn't have an exclusivity agreement over a job listing, he's going to want to edit your resume to remove your contact information at the very least. That's to make sure he gets paid. Plus, there is also the fact that some employers require the text of your resume to get cut and pasted into their database before they even look at it.
One thing you could to do is to only work with internal company recruiters, or 3rd party recruiters that have an exclusivity agreement with employers. Those recruiters are easy to identify. They usually have an email address (or a forwading email alias) from the domain name of the employer in question. And even if they don't, when they're communicating with you, they usually have no qualms about sharing the names of the client companies they're actively trying to hire for.
Of course, you could still work with 3rd party recruiters that don't have exclusivity, but may be you should ask for specific recommendations on who to trust from your friends, or from potential employers as soon as they tell you they've decided not to hire you.
One issue is that there are just too many third party recruiters these days. In this new age of internet, the barrier to entry is so low, anyone with an active phone line and a computer can claim to be a recruiter/manhunter. And you really do have to set up your own filters and not just trust anyone who contacts you with that claim.
And if non-exclusive 3rd party recruiters are coming up with job listings that you haven't seen yourself publicly listed by an employer yet, that only usually means that they're looking at a web site that you're not looking at yourself. In my case for instance, I found that many of the job listings I was interested in had been published by the companies themselves on Angel's list.
In your case, that web site is probably going to be different. It does vary based on your field, desired location, and desired company size, but my point is, that there is usually no secret proprietary database that recruiters use. Most of the time, they're just mining an aggregated form of publicly available information that doesn't cost anything to have access to.