Wrong.
The White House Records Office is about keeping track of employment records, not classified documents, meeting notes, etc.
Nothing gets recorded until a president sends it to NARA.
Here is the Records Office description.
{...
The
White House Records Office was a permanent office staffed by civil service employees who remained in their jobs over the course of many administrations. The office was responsible for recording official presidential actions, such as signing legislation and appointing individuals to government positions.
One of the main duties of the Records Office was to process the paperwork connected with the appointment of individuals to government positions. The staff transmitted the nomination to the
United States Congress if it required the confirmation of the
United States Senate and reported the status of the appointment to the government agencies concerned.
[1] The correspondence regarding the appointments was turned over to the
White House central files once the appointment process was completed, and was removed from the White House by the departing president at the end of the administration. ...}