That's interesting that they would suggest carbon based batteries.
Here's a quote from the Wikipedia article on AA batteries:
"Primary (non-rechargeable) zinc-carbon AA batteries of 400–900 milliamp-hours capacity are commonly made using Leclanché cell technology. Zinc-chloride batteries of 1000 to 1500 mAh are often sold as "long life" or "heavy duty". Alkaline batteries from 1700 mAh to almost 3000 mAh cost a little more, but last proportionally longer."
All single use AAs have a nominal voltage of 1.5V, so I am not sure why they would say zinc-carbon batteries are the best to use for long life of your toys. Zinc-carbon has the lowest mAh rating which means they have the shortest life of any of the AAs. One might try to claim that the lower rating means it provides less current, but the current draw is really based on the motor not on the battery.
Rechargeable batteries have a nominal voltage of 1.2 V, so they might not be able to provide the voltage that a given motor needs which may lead to an early death for the motor.