Short explanation: do something illegal on it, and you'll get caught.
The second an aws employee gets a call from the FBI who has a subpoena, they're gonna be shitting bricks, because its the fbi, and they're going to forward them everything they have on you; including your: credit card, IP address used to connect to the remote server, IP address used to register the account, your full name on file, your address, phone number, etc.