Merchants (such as Safeway) don't get this information if you use a credit card to make a purchase. The network (Visa, MC, Amex etc) authenticates the transaction and issuing bank releases the funds. But merchant doesn't even get the ZIP code of the customer.
If you make online purchases, most merchants do ask you to create an account (accept those 'enlightened ones that allow you guest sign-up), in which case they get all your information. There too you can use Paypal/Gwallet, if it is offered, but Paypal/Gwallet may or may not share the information with the merchant. That is kind of a grey area. Paypal clearly doesn't for merchants on ebay but in cases like Homedepot, I am not so sure.
The problem is that he is comfortable with Google receiving his information (name, address, email) but not third party developers selling through Google.
Developers on Google Play should not be merchants. Google should be more than a payment processor — especially if they are going to take 30% just like Apple does.
Apple handles this a hell of a lot better: as a developer you don't see anything about your customers (except how many there are per country) and you don't have to compute and collect sales tax yourself for every region you sell in, nor do you have to manually handle returns.
I hear the Amazon App Store does this a lot better than Google Play.
While I agree that Google's cut should be thinner, it works out way better as a buyer when you can ask a developer directly for a refund or about payment issues rather than deal with a huge company with automated customer service that doesn't work.
It's fairly straightforward to get a refund from Apple for an App Store app — we see about 2-3 refunds a week processed for our main app ($9.99).
The thing is, as developers, we don't have to deal with it. The customer is unhappy and gets their refund, Apple does it, not us. We simply see that a refund happened and move on.
It's a far better system for all involved: consistent refund policy for the customer, developer doesn't have to deal with it.
I do make those purchases sparingly and when I do so I consent to giving the merchant that information. Never have I consented to giving my information to developers.