President Obama defended his government as "the most transparent administration in history" Thursday afternoon during a White House "fireside hangout" hosted online by Google -- even as dozens of unanswered questions surrounding the decision-making process behind his assassination-by-drone program make the rounds in the news.

The president made the comment as he answered a question from Kira Davis, a conservative blogger and actress who was one of five participants in the session. She noted that with the recently leaked Justice Department memos regarding drone assassinations of American citizens and the Republican-driven Congressional investigation into the events leading up to the terrorist attack in Benghazi, "it just feels a lot less transparent than we all hoped it would be."

Obama immediately pushed back.

"Well, actually, on a whole bunch of fronts, we've kept that promise," he said. "This is the most transparent administration in history, and I can document how that is the case -- everything from every visitor who comes into the White House is now part of the public record. That is something we changed. Every law that we pass, every rule that we implement we put online for everyone to see."

But he did acknowledge that the administration still has work to do when it comes to informing the public about the U.S. military's use of drones to kill suspected terrorists -- even if they're American citizens.

"Part of what I'm going to have to work with Congress on is to make sure that whatever it is that we're providing Congress, that we have the mechanisms to also makes sure that the public understands what's going on, what the constraints are, what the legal parameters are, and that's something I take very seriously," he said. "I am not somebody who believes that the president has the authority to do whatever he wants, or whatever she wants whenever they want just under the guise of counterterrorism."

A bipartisan group of senators has been demanding answers to the legal justifications behind the drone assassinations after a Justice Department "white paper" on the subject was leaked early last week to NBC News' National Investigative Correspondent Michael Isikoff.

"When it comes to how we conduct counterterrorism, there are legitimate questions there, and we should have that debate," Obama told Davis. "And what I tried to do coming into the office was to create a legal and policy framework that respected our traditions and rule of law, but some of these programs are still classified, which meant that we might have shared them with the congressional intelligence office, but they're not on the front of the papers."

The leaked white paper lays out the condition under which U.S. forces could be justified in carrying out the attacks. There must be an 'imminent' threat of an attack against the United States, but officials would not have to present any hard evidence of such an attack. And it would have to be infeasible or too dangerous for U.S. forces to capture the suspects, according to Isikoff's story.

But the administration has hardly been forthcoming about the program and how it works. Ironically, it was in last year's Google+ Hangout that President Obama even first acknowledged that the U.S. was using drones in Afghanistan.

As The New York Times' Public Editor Margaret Sullivan points out, the Bureau of Investigative Journalism in the U.K. has discovered that within "the first three years after Obama took office, between 285 and 535 civilians were credibly reported killed by drone strikes -- including more than 60 children." And the Times itself has reported on the chilling high school year-book like "kill list" of suspected terrorists.

And she quotes the New York University School of Law's human rights investigator Sarah Knuckey stating the obvious problem in this situation.

“The U.S. is creating a precedent by carrying out strikes in secrecy without accountability to anyone,” Ms. Knuckey said. “What if all countries did what the U.S. is doing?”

The White House has since told the DOJ to release its legal justifications for the drone killings of the Americans to both the House and Senate Intelligence Committees.

On the White House visitor logs, Obama has been criticized too by the Center for Public Integrity for its spotty record-keeping. And as detailed by this round-up report last year by the Electronic Frontier Foundation's activist Trevor Timm, the Obama administration's record on responding to, and evading Freedom of Information Act requests is abysmal.

Obama spent under an hour answering questions on everything from government transparency and the need for computer coding literacy in high schools to what one couple should name their child.

The choice: Eleanor and Alice?

Obama dodged that one, joking that if the couple ended up choosing the one that he didn't pick, the kid might be traumatized for the rest of her life thinking that the president didn't like her name.

"Now if it's a boy, and you want to name him Barack, that's fine" he said.