Recycling Pizza Boxes

Every Friday, my school orders 20 pizzas. They come in a cardboard box. It's not coated with wax, so no worries there. We pass out tons of pizza and then toss the boxes in the trash (gasp!) OR we have this kind of face-off:

Rule Girl: Pizza boxes can't be recycled.
Green teacher: We can tear off the tops and recycle them. Those don't have any cheese or grease.
Green mom: Some of the bottoms don't have any grease either. Let's recycle those too!

After Green mom left, Green teachers (there were 3) were getting the cardboard ready for the bin and found several boxes that did (!) have grease on them. Ahhhh... the slippery slope. So I thought I'd find out what the real deal is on pizza boxes.

According to Earth911, pizza boxes CAN be recycled as long as you tear off any parts that have grease or food on them. The top of the box can usually be torn off and recycled with no problem.

According to the City of Austin recycling website, pizza boxes and any cardboard with food residue, should go in the garbage. I also checked another City of Austin site, in which you can look up things alphabetically. Under "P" for pizza, it says:
"Solid Waste Services cannot recycle pizza boxes due to food and grease contamination. Please put pizza boxes in your garbage cart."

Hmmmm... what a quandry.

Apparently, the people who sneak in contaminated boxes cause a problem. The grease and food contaminates the materials, causing wasted materials and money.

While searching around, I happened upon a pizza chain called Pizza Fusion, which offers a discount if you bring back your pizza box. Reusing. Interesting.

The conclusion seems to be that the City of Austin does NOT accept pizza boxes. Having seen what happened at school last week, I understand why. But it still seems okay to me to pull of the clean tops and recycle those. Of course, the boxes could be shredded or torn up for compost. But that's a lot of tearing during a 20 minute lunch period.

Any thoughts?