That's probably the right advice, you don't have to be cautious, you can look for work while in H-4 status (or while an applicant for H-4 status). The issue is

That's probably the right advice, you don't have to be cautious, you can look for work while in H-4 status (or while an applicant for H-4 status). The issue is this: if you find a new H-1B employer before your H-4 change of status application has been approved, while the new H-1B employer can file an H-1B petition for you, upon approval you likely will have to depart the U.S. and reenter with a new visa (if your previous H-1B visa has expired) or reenter with your previous still-valid visa and new H-1B approval notice. The point is this: USCIS likely will consider you ineligible for a change of status to H-1B when your underlying status is not H-4 but an applicant for H-4 status.