In some ways, I see this as a breach of trust; I can trust Google with some of my data but I dont think every app developer is worthy of even a certain percentage of that trust.
Holding this particular kind of transaction up as (no joke: your words) a "breach of trust" is just ridiculous on its face. So much so that frankly I suspect this is just yet another "Apple vs. Google" flame war in clever disguise.
Again, I agree there's an interesting discussion to be had about this stuff. But only if you give up the absurd absolutist flaming.
Most financial transactions do involve exchange of identifiable information; that remains true for online as as well as real world transactions; you are absolutely right about that. However, in all those transaction, you 'choose' to share some amount of information. One of the reasons services like Paypal became popular was the implicit lack of trust in an online transaction; people were more willing to trust an intermediary to keep their credit card information secure, than using it with any and all online merchants. Similarly, I trust Google as a company more than most other companies with my data and that's a 'choice' I made; however, them sharing certain parts of my identity with a multitude of app developers does seem to be something I didn't 'choose' to do. That seems to be a decision that Google took on my behalf and therein lies the "breach of trust" that you seem to have taken an exception to.
There is no flaming involved; I just think Google can do better.
However, I can appreciate the other side of this argument, and I think you are failing to draw the analogy the way a normal user would: when you purchase something online from Amazon, do you expect the manufacturer to know who you are? I would actually be very surprised if that is true right now.
How about when you purchase something, twenty years ago, in person, from K-Mart; do you expect the people who made the product you are purchasing to know who you are? Sure, it is clear that the K-Mart employee talking to you does, and it is clear that K-Mart's credit card computer does, but the manufacturer?
Further, while many people probably didn't realize this, it is clear that K-Mart's computer could (although it probably didn't twenty years ago; almost certainly did ten years ago) keep track of exactly what was purchased, and by whom using what credit cards, for their own data analysis and optimization.
But, would you ever have expected K-Mart to put together a massive list of all of the information on all of the people who purchased the shampoo you bought, and then send it to the shampoo company? If you did, I'm pretty certain you would be in the minority, even with today's technology.