So you're going to whitelist every mortgage broker, car dealer, apartment manager, etc who might need to pull a credit report? Doesn't sound practical.
No, not like that. You have a delivery service for your credit reports, which can make outgoing connections as it pleases, that ensures every credit report it delivers is paid for. You invoke it from inside your network, sending it the credit report along with the transaction number. It looks up that transaction to figure out where it needs to deliver the credit report. It doesn't have access to read any of the raw data.
Won't be perfectly secure, but it diminishes a major area of risk.
(There are other architectures that will accomplish the same thing, the key is that if a machine can access the user databases, you should be drastically limiting what kind of outgoing connections it can make.)