The bits that need to fall into place are:
- the LEOs need to be able to subpoena that information from Twitter (that bit's easy if you're talking about the FBI, they're in the same country as Twitter and have the right to get that subpoena)
- Twitter needs to have stored the relevant information (they probably do, at least, log what address any tweet was posted from, and its location is available when users opt in to that)
- the LEOs needs to be able to make use of the information. This is where it starts to fall down. What if the computer that communicated with Twitter was a Tor exit node, a proxy in the Ukraine or a compromised high school desktop in South Korea? The problem has been pushed back a level: the LEOs now need to go to the next service and try and match an individual to the information they have. If that's an ISP in the same country, this is possible but time-consuming. If it's a foreign or international organisation they might not have the ability.
By the way, whether you think such activities are illegal is not as relevant as whether the law specifically proscribes them. My understanding of U.S. Law (and I'm no expert) is that AnonOps have broken some computer misuse laws.