I don't think you're wrong per-se… I think that's one way of looking at it and is the way preferred by most people. It's nice to be a customer. You have power and control.
In this case, I would argue that you're bartering your attention for a service. To me the word customer implies an exchange of money - almost by definition. As I mentioned in my raw materials comment, Google turns around and sells your attention to advertisers: their real customers. They need you, but not in the same way they need their customers.
I voted your comment back to 1. I don't agree with your viewpoint, but I don't think it's a wrong viewpoint.
I don't think I understand what you mean... Do you mean swapping the roles via inverting the sense of "giver of something of value" and "provider of service"? As in:
"I provide Google the service of access to my personal data, and they give me use of Gmail as a payment, therefore Google is my customer."
"I provide my vendor the service of access to currency, and they give me a product as a payment, therefore my vendor is my customer."
That seems like a stretch, so I must be missing something.
I've been getting these infinite loops at login in gmail about once a week now. It's getting ridiculous. Google, please fix this. Sometimes clearing cookies doesn't even help