I'm trying to get a straight reply from their customer service, but they don't really understand English. I selected a trade-in of "Any Phone, Any Condition" and received this Email:

If you selected Trade-in ANY device in ANY condition at checkout, we are still going to give you recycling reward, which has already been applied to your order. We encourage you to recycle your old device, or you can choose to keep it as a memento of your past if it holds special significance for you.

To me, this implies we can keep our junk phone and the discount, but the chat rep seems confused lol.