I don't know if they got the memo that paper comes from sustainable tree farms that plant trees. Pretty sure Weyerhauser isn't flying down to South America to chop down virgin rainforests.
I'd attack the horrifyingly wasteful, and deceptively un-recyclable bottling industry. Depending on the recycling capabilities of your area, if you throw away plastic soda bottles with the cap on, it very well could go into the landfill.