Not true. Anyone can accept donations, in the US anyway. (Are there really other countries that prevent you from giving money to someone?).
The receiver will have to pay income taxes on the donations; and the giver will not be able to deduct the donation on their own income taxes. That's what requires special status.
This actually makes me realize I never thought about how people have to pay income tax on what they receive via kickstarter; I can't think of any reason they wouldn't. http://www.kickstarter.com/help/taxes
Assuming the people running the kickstarter campaigns are running a business, they only need to pay taxes on net income. I imagine most kickstarter campaigns go through the money fairly quickly so that's probably not typically a problem.