So is McDonalds a drink company? It makes most of its money from drinks...
The way a company makes its money is only weakly correlated to the service it offers to users. Think about it: if McDonalds stopped selling food, it would not have any customers. If Google stopped offering search, it would not have any users.
If we're going to simplify or generalize, I would simplify McDonald's to being a "sugar and salt" company. Those are the cravings in the human brain that it satisfies.
But yeah, I agree with you. Businesses are more complex than individual touchpoints.
Google is a ad company who uses search to attract customers.
I don't see the McDonald's reference as the same, drinks are part of their food product. Ads are not a integrated part of search (google did not start out having ads).
If your magazine starts handling ads in every other publisher's magazines too and then starts handling ads in TV and then starts putting up billboards by the highways, I'd say the answer isn't so obvious.
The way a company makes its money is only weakly correlated to the service it offers to users. Think about it: if McDonalds stopped selling food, it would not have any customers. If Google stopped offering search, it would not have any users.