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.