Should I Take That Literally?

I have discovered a couple of recycling Dumpsters for the public to use near my house. The trick is that they're both labelled "newspaper only". I wonder if they literally mean only newsprint is allowed. That doesn't make much sense to me--I mean, there is a lot of paper out there to be recycled and it would be a shame to only collect actual newspapers. (Especially since the print newspaper is a rapidly dying convention.)

I'm going to operate on the assumption that all paper is welcome except, you know, gross things like used paper towels and toilet paper. But that still leaves me wondering where to recycle my cardboard. I have a decent stack of flattened cereal boxes and the like. I know it's recyclable, the question is where? And do I dare leave it in the "newspaper only" Dumpster? The really sad part is that I'm overly rule-abiding and leaving cardboard in a paper-only recycling container makes me feel all civil disobedient-y, like Thoreau.  Pathetic, isn't it? 

For the record, "Dumpster" is a trademarked brand name and should always be capitalized. It's like Kleenex or Xerox that way.