Should an experienced third party recruiter with a specific search assignment focus his/her calls on candidates that closely meet the spec or a broader based approach using the "Who do you know that does this kind of work?" approach with a broader audience?
Why make it harder than it has to be? If you have the option of calling candidates who match the spec that seems a better use of time than calling people who don't match it hoping they know someone who does it.....that seems backwards to me. Now, if you don't have any candidates who closely match, then it makes sense to broaden and start digging for more referrals.