People referred to them as "No Such Agency" for a long time. It's kind of nice to see how they went from extreme public obscurity to a household name; it's hard to stay clandestine when even Joe Nobody knows who you are and exactly what you do.
Laws surrounding murder by and large aren't all that important. If it wasn't illegal you'd just have mob justice filling the gap, as murder is generally frowned upon quite severely by society.
Ideas surrounding freedom, liberty, and privacy are very complex, easily confused, and often forgotten until its too late. The laws around these things are mechanisms which help protect what you're country supposedly holds dare.
But in answer to your actual question, would you believe them if they said they hadn't?
It's unlikely that that would happen, unless we suddenly get a new president in the coming years who is unlike the rest and vehemently anti-domestic surveillance.
They might undergo some reform, but the government apparatus has been far too reliant on many aspects of their work to actually shut them down.
