Ask HN: Can Amazon go after my credit?

I've come across an issue ordering from Amazon. I initially bought a Playstation 3 from Amazon which suddenly broke hours after using it. So I went online to Amazon and I scheduled a free UPS pickup to get it replaced. When UPS arrived at my house the next day I told them that I had mistakenly thrown away the original box and I would not be returning my item. But it didn't end there. Today I woke up to a brand new package with a Playstation 3 and I haven't returned my old one! The Amazon page for replacement says credit card verification is required (which it wasn't) and my account has no payment credentials attached, I used gift cards. But according to Amazon - after 30 days they charge your credit card if the item is not returned.

So can Amazon legally bill me by mail or go after my credit for not returning these items even though they failed to take my credit card information?

Edit: I'm not trying to scam Amazon, I'm just curious why they would do something like this when there are millions of people out there that would take advantage of them.