I find it odd that we still do this. I know that I am not, by policy, able to give people who have worked for me any reference anymore other than to confirm they worked here from X to X and that they left in good standing.
The HR world is much too painfully strict on this stuff anymore, so I don't put much weight into references. Particularly because if someone will give me a reference, generally they LOVE the person. If I can't ask your previous employer any questions, do I really care that your best friends husband thinks you are a solid hire?