Imagine you just found out you won $25,000 in the lottery. You get a receipt — but in your haste, you actually leave the ticket at the store.

Disagree.  In fact, if she got a receipt for the winning ticket after validation, how did the clerks cash it in at Lottery Headquarters? 

I'm not stupid, but am I missing something here?  When you scan a ticket, doesn't it have a bar code that is read?  Then the terminal indicates "winner or no winner" so how can it be scanned and processed AFTER a receipt has been issued for the same ticket?

American Heritage Dictionary:

 re·ceipt    (ri-set')  n. 

"A written acknowledgment that a specified article, sum of money, or shipment of merchandise has been received."

If I went into a store and got $70 for 4/6 number in Lotto, even if I got the ticket back, I wouldn't be able to collect another $70 because that ticket had been scanned and paid.  What good is a receipt showing you won $25,000 if anyone else can cash it in without the receipt or another receipt can be printed? 

Please explain.  I think the New York Lottery owes this woman the entire $25,000 prize.  Didn't she do exactly what she was supposed to do, that is, go to a retailer and validate the ticket?  Sure she should have taken the ticket, but we all do mindless things when we are excited. We wouldn't be human if we didn't.  Don't blame the victim in this case.

Let's think about this, given the info in the OP.

If the whole thing is on surveillance tapes, the clerks acknowledged the ticket was a winner, thus they know that the player was the rightful winner.

Having that knowledge, the player wins the money, and the clerk and accomplices crank out license plates.

This is goung to be another one of those threads where, if the people saying "It's her fault" were her, they'd be screaming like banshees.

The ticket wasn't paid, so it was still a valid ticket that was payable at one of the lottery's offices. Past stories indicate that sometimes when a store clerk only checks a winning ticket they can void it as if it had been paid, but that can't be done for a ticket that has to be redeemed at a lottery office unless there's something seriously wrong with the system. As far as the "receipt," you obviously don't leave an unpaid ticket at a store that can't pay it (at least not deliberately), so what would you get a receipt for? Lottery retailers have claim forms for tickets that can't be redeemed at the store, and it's possible that the form can be printed with some information indicating that the ticket was checked and appears to be a winner.  Perhaps that's what the the woman got. At any rate, whatever she may have gotten from the store didn't invalidate the ticket and wasn't necessary for submitting the ticket and claiming the prize.

Okay, then perhaps the article was referring to something other than an actual receipt for the prize.  It just doesn't sound as if the Lottery Office did its homework before paying off the clerks.  After all, how would the thieves know where it was originally purchased?  The article indicates to me that the ticket wasn't purchased at the Mobil Station, just that the woman walked in to check them.  The article reads: New York State Lottery and the GTECH, their parent security firm — it's impenetrable, there's no way that anyone's going to get away with cashing a lottery ticket of that sum and get away with it,"  This statement doesn't make any sense to me.  Why cash the ticket in the first place? It sounds as if they did get away with it, only the real winner came forward to complain.  Maybe that's when they began to do their investigation and ask questions.  Just sounded to me like a screw up on the Lottery's part.

Welcome to the world of news reporting. She definitely didn't buy the ticket during that visit, because it's a raffle game, but there's nothing in the article to suggest she did or didn't buy it there when they were on sale. Perhaps she mentioned where she bought it, perhaps the lottery didn't bother asking, or perhaps they claimed it was a gift.

IMHO, the NY lottery has at least one huge  flaw in their security procedures for online games. The exact time the ticket is issued is printed on the ticket. There's also an identification number  that indicates which retailer. That info will all be in the database on the lottery's computers, so there's absolutely no reason to have that info printed clearly on the ticket. As a prevention against forgery the tickets already have info that's specific to that ticket. It's obviously possible for somebody to receive a winning ticket as a gift from somebody they don't really know, so the claimant can't be required to know when and where the ticket was bought, but the lottery can afford to be slightly suspicious about those cases.

I agree that the bit about the security being impenetrable doesn't make sense. This story is a good example of the real reason that the tickets warn that they are bearer instruments.  The lottery has no idea who bought a winning ticket  so there is a presumption that the person presenting a ticket to claim a prize is the owner. Most of the time that will be true, but now and then the person claiming the ticket won't be the owner, and the lottery usually won't have any way of knowing. Again, the story isn't very clear, but it sounds like the clerks acknowledged that the woman had presented the winning ticket to have it checked. If they had simply denied the woman's claims she may not have had any way to prove that the ticket was hers. Of course the clerks haven't gone to trial and after talking with a lawyer their version may well change.