you are wrong

- An H-1 or L-1 holder who has entered the U.S. with an advance parole document may depart and return as an H-1 or L-1 holder if that status has not expired.

This is saying you have AP, but you can enter with H1 (you have to apply it, or enter with the existing H1 visa). This mean you actually didnot use AP (not stamp on AP).


- An H-1 or L-1 holder who travels out of the United States, and returns on advance parole, is authorized to continue working for the H-1 or L-1 employer. He/she would not be required to obtain an EAD to work for this same employer, within the validity dates of the H-1 or L-1 petition approval.

If you current H1 expires, you cannot get H1 extension, you have to use EAD.