That is wrong also.
A fast food restaurant cannot put their trash bags in the paper recycling bin, no, but a few pizza boxes are not going contaminate an entire batch of recycled paper, unlike plastic where dissimilar plastics will contaminate and entire batch.
Paper recycling handles food residue without a problem. To recycle paper you throw it all in a gigantic vat, boil it, and everything breaks down. Inks, Fat, Oil and grease float to the top and are skimmed off, solids like staples and plastic are filtered out.
Unlike plastic where there is no economical way to remove the inks used to make white/blue/green containers and if you mix PET and ABS, you get garbage.