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.
But yeah, I agree with you. Businesses are more complex than individual touchpoints.
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 someone asks, which of the 2 answers would be more helpful to them?
eg: http://www.businessinsider.com/movie-concessions-drive-amc-e...
Yup don't say "Taylor Swift is in the online concert tickets business", she is in the music business.
McDonald's not in the hamburgers-and-cokes business, its in the fast food business.
Just because it's the way they make money it doesn't mean is the most appropriate classification.