"The agency was formally established by Truman in a memorandum of October 24, 1952, that revised National Security Council Intelligence Directive (NSCID) 9.[28] Since President Truman's memo was a classified document,[28] the existence of the NSA was not known to the public at that time."
I believe that you are correct that the NSA was originally an agency created by unilateral Presidential action that could have been disbanded by discretionary Presidential action, however, AFAICT, it has been a regular statutory agency since the adoption of the National Security Agency Act of 1959. [0]
I don't know what the legal status is now, but the NSA's origin sounds kind of like that: https://en.wikipedia.org/wiki/National_Security_Agency#World...
"The agency was formally established by Truman in a memorandum of October 24, 1952, that revised National Security Council Intelligence Directive (NSCID) 9.[28] Since President Truman's memo was a classified document,[28] the existence of the NSA was not known to the public at that time."
Here is that memo, according to the NSA: https://www.nsa.gov/public_info/_files/truman/truman_memo.pd... It seems odd to me in talking about the "Director of the NSA" instead of the agency itself, but what do I know.