At least where I live even the interior lining and lid are now made from cellulose fibers and as such the packaging is (a) fully renewable and (b) the materials can be reused for other paper-esque products.
Making matters worse is that half the statistics that would show the abysmal rate count "thermally recycled" (=burning it) towards the same metric and are thus pretty meaningless.
In Sweden, where I live, 78.5% of paper packaging put into the market was recycled for materials (as opposed to recycled for energy a.k.a burning it in a power plant)