Something I learned recently as my students were writing reports:
If you throw a water bottle into the recycling, you should remove the lid. The lids aren't recyclable (don't ask me why 'cause I don't remember), and the people who separate the items don't take time to unscrew the lids ... thus, a water bottle with a screwed-on lid will end up being shuffled over to the trash can. I can't quite bring myself to throw the lids in the trash can (they ARE plastic, after all), so I throw them in separately now.
As for the original question, I suspect it varies depending upon the area. For example, where I used to live, we were required to separate our recyclables ourselves: Paper, plastic, whatever. Where I live now, we throw it all into one big trash can, and it's collected at ... okay, I don't know where, but not my house. Since the recyclables are collected differently, it seems logical that different processing plants would treat non-recyclables differently.
Related question: I recycle everything I can, but for certain items like peanut butter jars that are extremely hard to clean, is it better to just throw away the jar than to use a bunch of water cleaning it out?
Serious answer: Get a dog to lick it out. Dogs are insane for peanut butter, and they'll be glad to clean out your jars.