If they can show probable cause that the owner of the account broke federal law, they have legal grounds to demand Twitter release his information.
But unless he has released classified information via the account, I'm not sure what law they'll be able to allege he violated.
It's definitely a stretch.
They have a legal mechanism, too. It's called a subpoena. If I understand correctly, they didn't use that here.
Look, I care about limiting the power of the Federal government to the parameters outlined in the law and the Constitution. I do not care how hard that makes their lives. I do not care that it crimps their ability to go get any information that they want. They have rules that their supposed to follow. If they want the information, they should go follow them.