I assume it's because they want the SEO juice and Google frowns on showing different content to the Googlebot vs a human being, but they also want their users to make more connections. So, they sometimes show more content to logged-out visitors.
Not just because of SEO, although that's one reason. Logged in users are already sold on LinkedIn, so LinkedIn wants to encourage them to make more connections. The aim for guest visitors is to get them to sign-up, so showing them a more useful page is a better way of showing what value LinkedIn can offer them.
Interesting. Someone should build a browser add in that shows logged out views of LinkedIn profiles even if the user is logged in, with the ability to toggle between the two views.
