They reason they want references is because part of the service that they provide their clients is to have checked references on candidates that they are going to present to them.
All clients want the reference done and some ask the recruiters to quote what was said on the references. Recruiters can't go around this policy, or are not supposed to because hypothetically, if they place someone at a company and that person winds up stealing money, for instance, they are not held accountable in any way because the references were done. This is why it's very important for everyone to stay in touch with former managers and upon leaving a job, ask them for their cell or home number or personal email address, in case they leave the company. You need to be able to locate them and ask them to supply references for you.
If they won't the thinking is that they're not comfortable doing it for some reason and that's a red flag. Just because someone interviews well and has stellar skills, does not mean that they have a good work ethic, or were dependable. The fact of the matter is that if a valued employee leaves a company, the manager will want to help that person land their next job.