The iPad (3) 30 day support clock seems to start on the day you "register" the product, not the day the product is purchased. I confirmed this when I setup a Genius Bar appointment and got the inspection required to purchase AppleCare + (includes accidental damage with deductible). Regarding getting the older AppleCare, I tried to do this on an iPhone4 which was under 1 year old, but obviously over the 30 days. I got 3 different results when trying to by AppleCare. 1) its past 30 days, sorry no AppleCare Plus. 2) we don't sell AppleCare anymore, and 3) I was told that since the iPhone4 was purchased before the new AppleCare Plus program started, I should still be able to get AppleCare (not Plus), but calling Apple Customer Service.
AppleCare Plus is the version that covers accidential damage, vs just warranty work. So this is why there needs to be an inspection (of a product taken out of an AppleStore). That's why you can buy AppleCare Plus on-line when you buy a new iPhone or iPad. So, if you have an older, but under 1 year old product, you might be able to get regular AppleCare warranty extended coverage.
I have also used a mail order repair (in Cupertino) for an iPhone 4 with water damage. They specialize in water damage and cracked screens. Cost was $99 plus shipping and they recovered a "dead" water soaked phone by a take apart and cleaning process, they also replace the battery and all the interior seals. But they do not replace the 2 water sensors - which are still red now. They also repair cracked iPad screens (for about double the iPhone 4 screen price).