This advice works for a lot of companies, but I've seen it work first hand to get a job interview at LinkedIn. In my short time at LinkedIn, I've referred two people for jobs and one of them got the job and the other one is in process. Both of the people I referred were interviewed promptly after my referral.
|This is my buddy John, I referred him to LinkedIn and now he sits behind me.
In general, referrals from current employees are much more likely to be seen by a recruiter, than from applying online. It should be no surprise that this is particularly important at LinkedIn where one of the 5 dimensions of the culture is "relationships matter." To learn more about what that means, check out this post from LinkedIn's founder Reid Hoffman. A referral is really key to getting an interview at LinkedIn.
*As usual, this is my personal opinion and not representing LinkedIn the company.