LinkedIn is a massive gold mine for headhunters. They can search millions of people by keyword. The more you have in your profile, the more headhunters will find you. If you are looking for a job, it may be in your best interest to get more people to look at your profile.
"There is no such thing as bad publicity"
The concept behind throwing everything on there is that while someone looking for an expert in sprockets may be disappointed that you were only at Spacely Sprockets for two years, if you excluded that from your profile they wouldn't have noticed that you are actually an expert in cogs they are looking for in another position.
Paper or 0101 0000 0110 1100 0110 0001 0111 0011 0111 0100 0110 1001 0110 0011?
Paper resumes are different because they are restricted by the format, the purpose, and silly HR quirks. They follow separate rules (and you leave out things not relevant to the position). If the company is doing their homework, excluding a job from your resume and your LinkedIn profile doesn't mean the company wouldn't find out about it during a background check. Chances are there is little harm from putting it on your LinkedIn -- anything deal-breaking they would likely find out anyway.
Focus on the Goal
Figure out what you want to do with your LinkedIn profile. Do you want to get headhunters to notice you? Then toss all your jobs in there so you'll match more keywords and get more eyes on your experience. Would you rather focus on getting headhunted only for jobs related to X, Y, and Z? Then only list skills related to X, Y, and Z.
At any rate, don't misrepresent yourself, your experience, or your abilities. While an employer may intentionally ignore your days spent working in an IT call center for money in college, they probably would be a lot less tolerant if you added a dozen skills you don't actually have just to get more hits.