I guess an example might be that the NSA has access to other partners information (e.g non-five eyes like Germany) and doesn't want their DB folks to be able to see that they are quering against the databases (e.g Merkels phone number)
This is exactly what PIR is for. A good intro is chapter 6 of the (awesome and ahead-of-its-time) book Malicious Cryptography. One of the authors works at the agency now, I believe.