LinkedIn does not require (or automatically redirect to) SSL. If you're not logged in, the homepage is served over https://. If you are logged in, typing linkedin.com brings you to your news feed, no redirect to https://. If you aren't logged in, then enter your username and password, you're redirected from the https:// site to the http:// one.
I strongly suggest using httpseverywhere for this reason. Although for some reason linkedin.com is listed as "buggy" by default :/ so enabling it might break some stuff.
Just tried it again, and yes, the main page works, but things like profile page and viewing the list of people who have recently viewed your profile give me blank pages.