Also the government is not all one monolithic entity. Just because the NSA has a backdoor doesnt mean theyll hand that information out to anyone who asks. Maybe if the CIA fills out a ton of paperwork, but if its the FBI theyll laugh in their faces and tell them the data doesnt exist.
Cause the FBI are the keystone cops of the intelligence world. Theres a reason they spun off a whole new agency rather than just give the FBI unlimited resources for the war on terror.