Let's say you're looking for a job and you (not a headhunter) send your resume in to a company. On your resume, you list your prior job experience - including a stint at the company you've just sent the resume to.
Now, knowing that the people that will be sorting/evaluating your resume/experience, don't you think it'd be a good idea that you can talk about your prior experience at that company? Like, for example, giving a name of someone you'd worked with and details about the projects on which you worked?
A friend just told me about an applicant that claimed to work at Company X, but when questioned could not recall a name or a detail. Worse yet, this person claimed to work in the NYC office when the department for whom they worked is/was/always will be based in NJ. And then this person got indignant when the hiring people checked with personnel about dates and salary (oddly enough, none of that information existed for this person, which was obviously a computer glitch!).
A true story to enliven your back-to-work Monday.