Correct. Google's real concern was not that people wouldn't use them as their favorite search engine; it was that relying on Apple and Microsoft to be stewards of access to the web was a huge business risk because, hypothetically, if Apple or Microsoft decided to block google.com at the browser level (or pick your favorite equivalent scenario, like failing to implement a standard that Google absolutely was going to be relying upon to provide service), Google was screwed.

Chrome was a business risk mitigation move.