Except the research doesn't really quite match that theory:
https://science.howstuffworks.com/environmental/green-science/paper-plastic1.htm
This gives both sides of the issue. Only big thing really missing from it is paper bags don't really biodegrade in landfills either, because that process takes oxygen and air flow, and the liners of the landfills are designed to prevent that (they want to reduce the release of methane since thats far worse for the environment).
http://www.allaboutbags.ca/typesofbags.html
I'm very pro doing whats environmentally friendly, but the whole "plastic is evil" thing is overblown because the alternatives are often just as evil if not more so. I myself use a mix of reusable and plastic bags because I feel thats what is actually best for the environment. I try to limit my plastic bag use to what I will use at least twice.