Why can't you get a detail Billing statement from a collection agency?

You can, but not directly from them. The debt collector is the agent of the original creditor and does not likely have all records of the debt or contract. The collector, as the agent of the creditor can go back to the creditor and request a reconciliation of payments and history, and will in fact be required to so that it van be verified if you notify the collector in writing that the debt is invalid due to payment or some other reason.