He is not google's customer.
I think you are. By this definition, I am a customer of Google, as is anyone in this thread who uses a Google service.
But I am not the final arbiter of meaning. The downvotes to my comment show that I am clearly wrong on this subject.
"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.
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.