Sure it is. But it's also nowhere near cost competitive and so no one does. They also don't even claim they're using anything else than "normal" HDPE made from ethylene distilled from crude oil.

They don't use "normal" HDPE, they use recycled HDPE which means they don't know what's inside their feedstock and it definitively means you can't get rid of the paper by burning it, because you're also burning whatever mystery chemicals remain inside.