Not really logical
If Twitter is going to make data publicly available then it makes no sense to make an exception of government agencies; and such an exception is not enforceable anyway as it's all too easy for agents to pose as private citizens. And that which is done in public (Twitter being effectively a public forum) is neither private nor confidential by definition.
I can't speak for anyone else, but what I object to is the doctrine that governments should have greater access to data than what is afforded others, except under the strictures of the Fourth Amendment and similar laws outside the US. If a court decides that there is probable cause to believe that private data contain evidence of specific wrongdoing then it may issue a warrant. Otherwise, the police and other government agencies should have the same access afforded the general public; no more and no less.