Right, but somebody has to maintain those IT systems, and if the government is anything like other huge, data-hoarding corporations, then they deploy sysadmins who have an incredible amount of access because they have to in order to maintain the system. IT systems do not run themselves.
Why do you need IT systems for a program that has allegedly been running covertly since a decade before Bletchley Park started building Colossus?
Let’s just presume that the people running this are recruited both for their competence and their ability to keep a secret. Would they immediately commission an IT team?
NSA needs IT. It’s essential. These programs - if they exist - are all about avoiding recording anything or communicating anything other than face to face.