I don't think Israel controlled the Rafah border in the start of the war which is when they made their declaration of not allowing aid.

They say that Israel didn't control it yet you couldn't go through it without their approval.

Correct. The first citation is from when Egypt and Palestinians controlled the border, the second is from later on when Israel controlled the Gaza side of the border. Egypt still controls the Egypt side of the border, regardless whether Israel or Palestine controls the Gaza side.