Here is a more specific answer.
June 1, 1999, INS published an interim rule regarding eligibility of H1 and L1 holders and their dependents to enter on the H or L visa status when traveling after filing the I-485. These foreign nationals do not have to apply for advance parole if they have a pending application for adjustment of status. It is only necessary for the examining inspector at the port of entry to confirm that the H or L holder is maintaining that status by still working for the correct petitioner as shown by the latest H or L approval notice, before allowing the H or L holder to enter the U.S. Therefore, the above issues pertaining to deferred inspection, etc. may not be applicable to a person who, for example, chooses to enter on the H1B or H-4 visa instead of using the AP.