Can the FBI/DOJ/whoever require me (or Twitter) to continue to send out the tweets? Or is it somehow illegal for me to set up such an account in the first place?
"At first glance, the Facebook profile is the perfect deception. Purportedly belonging to brown-haired woman named Sondra Prince, it shows her driving a car, splayed across a white BMW, hugging two young children. If someone were to stumble across the profile, which still exists, there would be little way for them to know the truth: The profile is a fake.
"It was created surreptitiously by a Drug Enforcement Administration agent, who seized Prince’s phone in July 2010 after arresting her, mined it for photographs, then used those pictures to forge a fraudulent profile which allowed authorities to impersonate Prince in an investigation into an alleged New York drug ring."
Also, yes, they are constrained by law. That's how we're able to take the government to court.