Just to chime in about this-I have a Nokia Lumia 928. I have a son, but he's only 8 months and doesn't play with my phone. However, my friends kids will sometimes ask if I can help them play Angry Birds, etc, since they know/noticed I know more games than their parents. So I have "Kid's Corner" set up on my phone. It's a special separate screen that lets you add games and apps that are restricted, perfect for when a little one asks to see the games on your phone.
While in "Kid's Corner", all IAP is disabled, and if you try to buy anything, a popup appears that says you have to exit Kids Corner for any purchases. You can't exit Kids Corner without my password.
We were at lunch with my nephew, and he asked if he could see my phone. I opened Kids Corner for him, and he was delighted he could "play" Angry Birds GO! (I put it in quotations because an almost 3-year old doesn't entirely understand the game, but he loved even checking out the animations). My brother-in-law was sitting next to him to help him, and my nephew tried to select a bird that was an IAP. Immediately, my brother-in-law tried to stop him, but I told them not to worry since they were blocked by Kids Corner. But this was literally a 2-second tap that would have purchased a .99 bird. If my brother-in-law had blinked he would have missed his son tapping "buy", and if this had been part of that 15-minute iOS window, I would have been the proud owner of a new Angry Birds Cart.
My point in this rambling story is that some IAPs are as quick as tapping "Buy", and unless you literally hover over a kid and never blink, there's a chance they'll slip one past you. My nephew is a smart kid, but there's no way he understood what he did. There was a button, it looked like if he clicked the button he got to be his favorite bird. So he tried to hit the button.
I think there's a huge difference between IAPs that are clearly a paid purchase and ones like in Angry Birds GO!, where everything blends together and little players can flip from an item that's included to one that's a purchase by scrolling. Obviously, you would hope parents might notice before it reaches thousands of dollars, but I could very easily see a child playing under the supervision of a parent and still buying stuff without anyone realizing. If the dollar price is designed to look graphically like the in-game currency, it might slip right by someone who doesn't even realize there's an IAP in the game.
So that's my .02 as a fairly new parent, but the "techy aunt/friend" for my nephew and friends kids. It's difficult to watch a kid every second they're on a game, and the games conspire to make real money purchases look and feel like fake money purchases...it's an unfortunate combo that leads to these kinds of issues.
Now, if you missed that your kid racked up $1,000 worth of IAPs, the kid either went wild on an especially sneaky game or there's no supervision. But small amounts can easily slip by, and I'm willing to bet for all the "ZOMG MY KID BLEW $10,000 ON CANDY CRUSH" headlines, there's a slew of parents who spent $2-3 extra because they didn't realize there was a window where IAPs didn't require a password. For $3 it's easier to shrug and say "Whoops, my bad-need to lock this down better" but the game companies make a fair bit extra from all those "little" mistakes.