Yes, you are supposed to give them your KTTW card. But sometimes, they just take your room number. Like when you're in the theater, just before a show, or if you're at the pool, and say something like "My DW has the key", they will write down your stateroom. They do have you sign a charge slip (gives you the chance to tip you know!), and they give you a paper copy of a receipt.
Now if you were a very sneaky type person, you could charge things to someone else. Assuming the mis-charged person was smart enough to check their bill, and wise enough to remember what they spent, mis-charged person would go to guest services and say "hey, I have a problem with the 5 drinks that were charged to me in the Walt Disney theater last night. They were during the early show, and I was at dinner then, so I couldn't have charged them."
DCL will probably remove the charges, and they will pull the paper record of the transaction. If this was simply a mistake (i.e. the mis-charger mixed up two of his room numbers), he would have signed his own name. DCL figures out who it is and fixes the charges.
I personally have never had anything mis-charged in my 3 cruises. A couple of times I had forgotten charges, and stopped by guest services. The first thing they do is pull up the record to see what was bought. Last time, it showed a charge from Mickey's Mate, and since I hadn't been in the store, I didn't think it was my charge. They pulled it up and said "Two sets of swim goggles, sold yesterday?" Oh yeah, I did buy googles up by the pool when my kids broke theirs.
Hope this helps you out.
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