This case was about users public profiles. LinkedIn makes users profiles accessible to the Googlebot and other public visitors without the need to login. There was an additional wrinkle in that HiQ actually had a commercial agreement with LinkedIn for some time that explicitly allowed them to scrape. They were arguing that canceling this agreement was anticompetitive and would destroy their entire business. Because of that pre-existing agreement, they likely didn't dwell on the distinction of public or private as they already set the precedent of signing up to an agreement that authorized them in the past, so they can't now say they never needed one in the first place.
I'm not sure why you are referring back to the specifics of the case since your comment was about what you put forward as a general framework required for scraping to be legal and that was what my comment was regarding.