Surprisingly this just isn't true. It takes a lot of work and chemicals to clean inks and glues out of paper for recycling.
Penn & Teller looked into this in an episode of Bullshit! a while back - https://www.youtube.com/watch?v=rExEVZlQia4
Aluminum and clear glass are very efficient to recycle, plastics and colored glass depend on commodity prices, and paper is just a terrible idea to recycle. It's much better for the environment to farm trees for making paper, then put that paper in landfills and harvest the methane gas the paper emits when it decomposes.