According to the PPWR rules, if you (as a webshop) package your shipment in non-branded box and send it from another EU country to another, then you are considered to be manufacturer(=you were the first to bring this into market) and EPR/PPWR rules apply. There is no exemption for this.
I'm more inclined to believe the person who backed up their argument with a citation, especially after looking at the document they linked which expressly contradicts you.
Sorry, messed up the terms here. You became producer. From the earlier faq that parent posted;
> The following provide some typical examples of who the producer of transport packaging is: - If Company A fills the cardboard boxes and sells them to an end user in another Member State, then Company A would typically be the producer in that other Member State.
> If Company A manufactures cardboard boxes under the name or trademark of Company B,
then Company B will typically become the manufacturer and producer of the boxes in that
Member State. However, if Company B is a micro-enterprise, then Company A is
manufacturer and the producer in the Member State.
That has the same "typically", so I'd assume it has the same micro-enterprise exemption. Otherwise only branded boxes would be exempt and that'd be pretty weird.