During signup, if you are on one of the major webmail services, it will explicitly ask you to authorize yourself on them so it can get your contacts however.
Having worked there and specifically as product manager for the Who Viewed My Profile portion, I can tell you that they take privacy very seriously.
But many people might interpret that as a LinkedIn log-in form (not realizing that they are already logged in). If LinkedIn just had an ad there asking people to click a button to then fill out their e-mail address/password, they would likely have much fewer people let LinkedIn look at their e-mail account.
This is much more legit than just trying the Linkedin account username/password to access the e-mail account, but it is still a form of phishing.
Linkedin will show you a login-like screen with your email address pre-populated and a password prompt. Two dangerous things can happen: 1) a user can absent-mindedly assume they're at their email login page and type in their email password (less likely) 2) a user can absent-mindedly assume that this is the Linkedin login page and type in their Linkedin password.
The problem with (1) (and 2 if your email password is the same as your linkedin password) is that you've just given Linkedin access to your email contact list. Then Linkedin can shoot an email to all your contacts letting them know you're on Linkedin / etc.
To me this is a form of phishing that countless less-tech-savvy folks are getting caught up in and should not be OKAY in the industry.