It is not true. This is something I had to learn from people that have been in high-level roles in government. I will start with the history and purpose of constitutions.
General guidelines to organize and plan governments around have existed since time immemorial. What makes modern constitutions special is that it specifies the idea of popular sovereignty, that it is the entirety of the population of a nation that provides the legitimacy for the state.
The idea originated amidst the Enlightenment period of the 17-1800s. Monarchy was where, generally speaking, legitimacy derived ultimately from the divinity of the ruler, and was passed down through their descendants. Popular sovereignty and the republican form of government that enshrined it had to be evolved over hundreds of years, the Dutch constitution being a pillar of the system. The US Constitution was a virtual carbon copy of the Dutch one.
One of the questions grappled with in the transition from monarchy to republic was, what happens when the government fails to exercise authority due to exigent circumstances? This question led to the modern concept of the "state of emergency" in which the government reverts to a more primitive form. It was also noted that protecting the republic required extra-legal powers, because republican forms of government are relatively easy to subvert.
When states of emergency arise, the constitution is set aside by the executive branch of government until order is restored. No elections are held, power rests in the hands of the military.
This is but one of the ways in which constitutions cannot be seen as the ultimate arbiters of the organization of society. If society can't protect itself, then somebody must protect society.
Now we can deal with the matter of intelligence services. Intelligence services were once crucial to the functioning of pre-republican states. They were called the secret police, the apparatus of government that takes care of the tasks that need to be done by the state but are too unsavory for the public to know about.
It is inevitable that the need for these tasks arise. This comment is already too long for me to give and flesh out examples. The biggest issue that needs dealing with is revolution, which is a violent event that we usually think of as originating from grassroots populism, but is also just as easily planned and carried out by small groups that can't be seen as the instrumentation of popular sovereignty. Discovering and dealing with these national threats is part of the purview of intelligence services. The alternative to secret police is endless revolutions of the kind seen by Latin America during the late 20th century.
Another function that must be dealt with is the exploration and research of matters too unsavory for the public to deal with, as these things can carry serious consequences for public safety. I have learned recently that the CIA has carried on with experiments carried out by the Nazis. This is but one example.
The people in national intelligence organizations see themselves as guardians of the people, and empowered with ultimate authority to do that. Many countries, most notably Eastern European ones, oscillate between secret-police control and a more feudal kind of organization. One system you might study is Russia's current system of tributary taxation.
Keeping state secrets secret is the true foundation of any national security functionary, as extremely serious consequences could theoretically result. And when you get to the scale of government, theoretically possible means you have to do a study to determine how many times and where it's actually happened, and to come up with plans for dealing with it when the theory finds manifestation
The main resource that has taught me this traditional point of view believes that Snowden is a bloody traitor and should be executed. This is opinion he offered freely on Quora, with no respect given to the popular view of Snowden as a hero. As far as he's concerned, Snowden needs to serve as an example, he absolutely has to die, even if he's revealed some atrocities and secret information.
This person has also revealed vast amounts of information that has been declassified, but still shows mind-blowing inadequacy of anything other than highly trained government functionaries to deal with the heavy weight of exercising legitimate force. The idea I think he's conveying is that while Snowden's revelations might be shocking and awful, his similar revelations cut to the meat of why such things are needed.
As far as this point of view is concerned, atrocities and subversion of popular sovereignty is business as usual in the government sphere, revealing them does society no good. They've always happened, they're always happening, let the people trained to deal with them do their jobs, just like any sphere of human org, the org learns how to do their jobs better over time.
We have dealt with the traditional view of how 'secret' organizations derive their legitimacy, now I will offer my speculation as to how to think about how to move forward.
I believe Edward Snowden represents a change in the ability of society to countenance the full weight of what humans are capable of. Consciousness is being raised in the human race across the board, and the old problems that gave rise to intelligence apparatus in the past are no longer relevant.
As a result, changes need to be made in how society is planned. The old ways of organizing society are still valid, they still work, and they will continue to work. The US government will happily kangaroo court Snowden as cruelly as they can if they ever get their hands on him. And high level government functionaries will say and believe that he deserves it.
Because what Snowden ultimately embodies, to this point of view, is the same kind of thought that leads to endless, pointless revolution, the idea that humanity cannot overcome its basic nature, and so will always require highly-trained operatives and apparatus to deal with it in secret like it needs to be dealt with.
This has to fundamentally be outside of the existing legal system and constitution, which concerns itself with limiting the powers of government so as to facilitate commerce and public expression, but is woefully inadequate to deal with the protection of that society. Secrecy is an essential tool, to be wielded cautiously and judiciously. The government is the only entity that reserves the right to compel labor other than overtly criminal organizations like organized crime.
We may demand changes in how secret government operations are conducted, but it may never come to pass that secrecy is totally eliminated from government. I have a greater appreciation for this mindset now than I used to, though I still hope that we can find a way to stop ridiculousness like the MKULTRA project.