I have no idea what Paypal is trying to achieve by passing on this fairly personal piece of data. I always have to enter a separate email address with the retailer anyway, and because of this scheme, those two of course never match.
For years the Paypal API sucked, and even today their are many companies that do not have full integration with paypal, so this is a way to match payment records as for 99% of shoppers the email address for the order/account will match the paypal email address.
Of course I let her know about it, and I seem to recall her saying she'd addressed it successfully, but if she described how, I no longer remember. It quite astonished me that this was even a thing that could happen, though. One hopes it no longer does.
It's like her giving out her email address and it being firstname.lastname@gmail.com
I'm not sure the fault lies with the service.
With chip and pin? I don't think they do.
Where I work you need the 3 digit security code and some address numbers (which you can make up) to properly process a transaction without the card.
Something to keep in mind is that when chip and PIN was developed to combat credit card fraud it was card present fraud that was the big problem, either by someone using the stolen card itself at a brick and mortar merchant or making a counterfeit cart by writing the stolen number onto a blank card and using that at a brick and mortar merchant. Card not present fraud, where the number is used but not a card such as at an online merchant or a mail order merchant or telephone order merchant, was much less common.
Chip and pin made card present fraud much harder because it was much harder to obtain blank chip cards and the equipment to write a stolen number to them, and it made using an actual stolen card harder because of the PIN.