Exactly. With no knowledge of who my information is going to I can't agree to submit an application. Privacy is one reason; not having your time wasted if the companies aren't something you're interested in is another.
That being said, I'm assuming you'll be told what company is interested in you (if any) when/if they make contact rather than the usual recruiter nonsense ie. "A company in the financial services space" etc etc
This way, you keep your site single-blind (to keep people from skipping using your service) and if a company happened to be in the list, the person could still use your service (just hiding his/her info from that party).