nope, wrong again. ARPUs for PayPal users are probably only around $5-25 per year (excluding the minority of fanatic eBay regulars), and you can easily eat up all of that cost or more in telephone customer support.
US-based customer services reps cannot complete a phone call for less than $7 fully loaded. You really, realllllly do not want to have a CS infrastructure taking multiple calls to resolve Mrs. Smith's inability to successfully use her computer when Mrs. Smith is probably going to be worth less than a buck fifty to you and will likely need more handholding next time, too.
A more likely case than relying on "maybe users will remember their passwords better" is that Facebook could capture a larger part of transactions (say 30% as App Store does) which enables them to better cover support and fraud.
Don't throw ARPUs at me. Either they are profitable or they are not.
I can certainly understand the argument that users of other sign-on systems "may" remember their passwords better than PayPal, but what evidence do you have of this? What extra margin of increased password remembrance makes for a more profitable model?
it was deemed to be "cheaper" to just not deal with a minority % of password recovery cases (that might also occasionally be fraud) than to provide high-cost customer support for low-value average users.
think about it: if you can cut a minority % of your customer base that causes a large % of the cost (or simply just more than they are worth) then you can make more money.
this wasn't such a big mistake in itself, except that PayPal probably didn't consider the network effect of negative brand damage due to not providing very good customer service for such a large # -- though still minority -- of users.
i'm saying this: 1) telephone support is expensive, and doesn't offset low-value ARPU 2)