Out of curiosity, why did he think Apple had far superior payment system? I personally think Apple's payment gateways no better than Amazon Checkout or Google Checkout experience.
Thus when buying on iOS it's always easier to use Apple's system because you're already half signed-in and they already have your credit card.
But yes, if you re-enter your credit card details then they are pretty much the same except for having to re-enter your details.
Have you ever thought that Android in app purchases are lower because they allow developers to use Paypal to buy stuff, and don't require a credit card to use the device?
The app (Kindle, GMail, etc) have your account so it has your payment details
1) Apple has more active credit cards than Amazon.
2) If someone were to purchase a book on an iOS device it is more likely they have an active credit card on their account than an Amazon account with an active credit card.
3) One payment system is easier for customers to understand and trust.
Steve's wording here may have indicated better technology in his mind, but I doubt that is true, given amazons incredible focus on taking credit card payments accurately and quickly. Reasonably though the reasons outlined above would be good reasons it was better overall, even if it really wasn't consumer friendly in the end because of the lock-in.
#3 is not something anyone believes, even you.
I'd counter with iTunes hysterically bad receipt notifications. Typically you get a receipt between 3 days to 2 weeks after you buy something. Every time I receive an iTunes receipt I have to strain to remember way back when I bought the thing the receipt is for.