If a company was exporting material from the US to the EU, they should be aware of the compliance status of the packaging material used for these products to this regulation, regardless if it is branded packaging or not. Is this correct?
It is always important to be aware of the regulations impacting any part of a product being shipped/imported even if you are not specifically responsible for the piece being imported. That way you can try to avoid any impacts because of violations for which you are not specifically responsible and guide the authorities back to the correct party if necessary. Often smaller companies are not aware of all the regulations or the locations to which you are shipping product containing their parts, so it is best to try to cover all bases and either make them aware of the need to be compliant or find another supplier for that part.