Okay, people like Voldemarv would be well advised to do a little bit of research before dispensing personal guesses:
From the USCIS
website (emphasis added):
Q : Who can an H-1B alien work for?
H-1B aliens may only work for the petitioning U.S. employer and only in the H-1B activities described in the petition. The petitioning U.S. employer may place the H-1B worker on the worksite of another employer if all applicable rules (e.g., Department of Labor rules) are followed. H-1B aliens may work for more than one U.S. employer, but must have a Form I-129 petition approved by each employer.
It is pretty clear, and well known, that if you work for any secondary employer who has not filed a I-129 on your behalf, you are in violation of H-1B status. While your work is still lawful by virtue of your EAD, you are not in H-1B status anymore. The lawyer was absolutely
not right.