That sounds to me like they're just trying to scare you into buying it when you buy the computer so you don't "forget" to buy it at a later date. If you never have to use the AppleCare, and I'm sure a large majority never do, then it is nothing but profit for them. That is why companies push extended warranties all the time.
So no, you're not missing out on anything.
Personally, I wouldn't get AppleCare. I would look for something that covers ADH (accidental damage from handling). A company called SquareTrade offers this. So far, they seem pretty reliable to me. I'm thinking about getting this for my MacBook Pro when I buy it. Of course, you don't get the student discount, but you can save by finding coupon codes online, and you also get the accidental damage coverage.
The Apple site makes it very confusing by urging people to buy AC when purchasing by stating "We recommend that you purchase the AppleCare Protection Plan when you purchase your Apple system to take maximum advantage of the coverage the plan provides."
To me that sounds like you are misssing out on SOMETHING if you don't purchase everything at the same time.
Aristobat, I am not challenging AT ALL, I just want to save a couple bucks now and make sure I am not missing out on anything, ya know. Being on a student budget is tough.