Your correct that in the real world things are different, in fact here are the real world court cases that in my opinion clearly define the activity of the Brave browser as not a copyright violation.

This case was about google getting money while displaying parts of copyrighted material. The court ruled it was fair use. (https://www.documentcloud.org/documents/834877-google-books-...)

This case ( still pending ) was about google being able to display parts of news stories without paying the authors ( the initial ruling was it was legal, but Germany was allowed to impose a "tax", current guidance is that even the tax may not be allowed and Google will be able to display the content ) https://www.nytimes.com/reuters/2018/12/13/technology/13reut...

Since you referenced people who had the same idea as Brave and it was found to be illegal, would you care to reference those specific cases ?