I can't see this happening.
I've got posts scattered all over this site throughout the years showcasing just how much I dislike eBay/PayPal and I'd love to see a competitor rise up and give them a run for their money (if not in the auction business, at least in the payment processing business which is exactly what this rumor relates to) but I just don't see Apple being the one to do it.
I had high hopes for Google Checkout, and it's nearly running on empty. If they can't do it with their user base and reputation, I don't think anyone can.
1. Why would people leave PayPal if they've already grown accustomed to using it? Yes, there may be ways for Apple to do this, but it would take much more effort and resources than they probably can afford to give the project.
2. Forget trying to sneak into the auction payment segment of the market. Google tried that and it went nowhere.
3. The big difference between eBay, Google, Western Union and the rest that have tried online payments and Apple is this: while none of those companies actually sell anything, Apple does. There would be direct conflict of interest in some (many?) markets. It doesn't make much sense to enter a new business that you can't fully saturate.
4. This isn't a new mouse or tablet or even phone (which has enough logistical issues of its own) - getting into online payments is nearly as complex as starting a bank. eBay still hasn't fully integrated the PayPal purchase and that happened half a decade ago. There's loads of red tape and government inquiries still floating around that purchase. I don't think Apple can just jump in; the iTunes infrastructure doesn't even give them a fraction of what they'd need to really make a run at this. Some people forget, but eBay had its own PayPal competitor back in the day and even they couldn't compete with PayPal and just purchased them outright.
Now unless Apple plans on purchasing eBay - which they don't even have enough cash to do, believe it or not - I think this is some analyst pipe dream that makes good rumor/gossip mill fodder but will end up going no where...