I believe you are forgetting who the customers of Google are. Hint, they're not you. The people who give money to Google are their customers - the advertisers.
Actually, both the free users of the search service AND the paid buyers of the advertising service are both customers of Google.
Just because you are providing the service for free, does not mean the buyer is not your customer.
Google is providing you a service if you use their search tool; it is the reason to visit their website and enter your search queries.
There is a related service being sold to various companies that choose to advertise.
But this doesn't exclude users of the other service from being a customer.
Just like if you buy a magazine, you are still a customer, even though there is another company paying to list ads in the magazine you read.
You are still a customer, even if your magazine is provided on a complimentary or promotional basis free of charge.