The reason for the copy is in case of a dispute over the passport stamp and log book, which is what happened to me. Luckily I had the receipt. But sounds like you were a cute American / Brit / Canuck/ Other?, so no shirt no shoes no problem (cash and sexual favors are helpful as well, I understand).
So, good for you for pulling off a 60 day stay for the price of 30 and and shame on them for allowing