Back on the subject of strollers being stolen at Disney parks, may I present rental stroller insurance:
What happens if my stroller is stolen?
Under our terms and conditions, you are responsible for the loss of the stroller during your rental period. The replacement cost for a single stroller is $225 and the replacement cost for a double stroller is $350.
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What is cost of the theft/damage insurance and what does it cover?
This insurance costs $25 for the length of your rental. It must be purchased prior to the delivery of your stroller. It will cover the cost of your stroller in the event that it is stolen or damaged during your rental.
http://www.magicstrollers.com/help/
Optional Rental Insurance covers the replacement cost of the Stroller and Accessories, in the event they are stolen or damaged.
http://www.babywheelsorlando.com/doublemini.html
Stroller theft (as well as theft from stroller) absolutely do occur, at least at the US Disney parks. I suspect that they are also occur at the non-US parks, even if strollers are not used as frequently.
As a disclaimer, I have no idea about the second company, but can definitely vouch for the integrity and honesty of the first, having a long relationship with their parent company and knowing the players personally. That isn't meant as a business advertisement, but rather as validation that they wouldn't be offering insurance unless it were potentially needed.
Then there is this comment which is just one of many, many online about stroller theft at Disney parks:
Yep it got stolen on our 2nd day there. It was labeled with our last name too. Disney was really great and tried to help locate it and even gave us strollers for our kids until we got a replacement. I dont think people realize that things including strollers get stolen everywhere even at Disney. That day at AK we were the 5th stroller reported stolen according the person helping us
I agree with the quote; I think that too often people think that just because they are at a Disney park that everything is sprinkled with pixie dust and that they can let their guard down.
My advice to anyone will continue to be not to leave anything of any value and/or importance in a stroller, and to expect that there is some likelihood of a stroller being stolen, and hence to consider taking one of lesser value.