When "we" decided to grant the government a monopoly on violence, there was nothing in the contract about letting them hack and sabotage American computer systems or commit other crimes at will.
But either way, "we" also didn't put anything in our "contract" that let them make nuclear weapons, air forces, computer inter-networks, or social security/welfare programs.
You're missing the word "presently."
That back door is there. Others not having figured out how to interact with it yet is a matter of security through obscurity[0], and the system is still weaker for it, even though it's not yet fully cracked.
[0] https://en.wikipedia.org/wiki/Security_through_obscurity