Personally I wouldn't volunteer to tell them which or how many big tech companies rejected my resume. I'm afraid that nine times out of ten it would create undue prejudice in the interviewer/recruiter.
Important to note that interviewer and recruiter are two different parties. The interviewer's job is to be skeptical of you; the recruiter's job is to polish you up and sell you to the interviewer. The recruiter is on your side, so it makes sense to be open with them.
(Note that this only applies to recruiting agencies. A "recruiter" at the company you're interviewing for is the exact opposite story.)
Thanks that is actually great advice. I added an addendum suggesting let agencies know he could use interview coaching but avoid details like where he's applied already or to how many companies.
