Read this: However, upon returning to the United States, you must present your valid H, L, K, or V nonimmigrant visa and continue to remain eligible for that status.
You still need H visa, and of course, if you have H visa, you do not need AP. That is not 驚訝 at all.
You still need H visa, and of course, if you have H visa, you do not need AP. That is not 驚訝 at all.