The accuracy requirement is about deliverability. If mail sent to your professional email address would also be delivered to you, you are in the clear. It is simply a different address to also reach you.
This post is provided for general informational purposes only and is not intended to be legal advice specific to you. This general information is not a substitute for the advice of an attorney in your jurisdiction. The attorney client relationship is not established by this post.
Using a forwarding email to send and receive emails by iself is not a violation of the law; sneding unsolicited emails from either account is where the problem exists.
This is not legal advice but a general comment on society based on a limited set of hypothetical circumstances. No one should act or refrain from acting based on these comments without seeking appropriately licensed legal or professional advice. The author disclaims all liability in respect to actions taken or not taken based on his comments.