That's likely because governments are increasingly catching on that social networks store a great deal of information about their users that could be useful to law enforcement, said Eva Galperin, international freedom of expression coordinator at the Electronic Frontier Foundation. The information sometimes includes physical location and political and social affiliations.

"It's really up to the companies to decide whether or not they're going to comply with requests for information, so they become these extremely powerful arbiters that are capable of de facto censorship," Galperin said.

The EFF gives Twitter higher marks than when it comes to being transparent about government requests and sticking up for its users in court. For instance, in a current case, it has [PDF] handing over its data on an Occupy Wall Street protester.

Protecting user privacy can be a good business strategy, according to Chris Conley, a technology and civil liberties attorney at the American Civil Liberties Union of Northern California.

Twitter "recognizes that users use Twitter not just because it's a great service, but also because they trust the company," he said.