I think they're committing the far too common sin of conflating coordination systems without objective physical reality or ontological primacy with lies. In their defense, I'll note that even the writers of the Constitution may have been doing the same thing but in reverse: using the royal "We" to refer to some nebulous conglomeration of residents on American territory instead of the more concrete and prosaic truth, that it was a far smaller group of men with varying degrees of endorsement from their nominal constituencies, in the midst of a civil war. 

The American Constitution is a "lie" in the same way that paper or digital money is a "lie". There is no objective value of a string of digits in your bank's servers. But objective value (if that's a thing) is often less important than the far more subjective but just-as-real ability to coordinate with other people. Money serves as a hard-to-counterfeit proof of your control over assets, with the weight of the State backing you up in extremis. Similarly, the Constitution has the weight of centuries and consensus behind it (and, nominally, an army). 

It creates a bright line in the sand: certain actions that are "unconstitutional" are recognized by everyone as being unacceptable and necessary to contest with legal or physical force. Even better? The Consistution is common knowledge, and knowledge of common knowledge. If someone breaches it, then, at least in theory, everyone knows they've done something bad, and the person breaching it won't even have plausible deniability about the matter. 

Of course, it's hardly that simple in practice, but the courts and executive exist to interpret and modify the document and keep it relevant, while acknowledging that until due process was used to modify it (an Amendment), it remains paramount. There might be legal kerfuffles about state vs federal rights, but only the maximally partisan would look at a (hypothetical example) of a ruling president putting on a crown and abolishing elections as Constitutional. 

In other words, the Constitution is a Schelling point, a bright line in the sand or a river that separates (many) bad actions from the good. It's not perfect, but it works well enough in practice. Other countries, such as the UK, have an "unwritten" Constitution, a system of both legibible/verbal and implicit tradition that is held as a check to the vagaries of politics or law. 

It can be dangerous at the symbolic level, in that political legitimacy needs to pretend to rest on something even if it is in practice circular. This is an is-ought gap problem: the government is legitimate because you obey the government without resistance (descriptive), and you obey the government without resistance because it is legitimate (normative). This second part is, yes, dependent on what one thinks about what makes the government legitimate. Embracing the circularity is unstable. A totalitarian state and a democracy would both be legitimate as long as people don't protest. But what if people do protest? You need an idea that will pull citizens to obey the government by default, even if it goes against their immediate self-interest, even if many others disagree.

In the US, the constitution is part of this stabilizing idea. It's not the only part, but it got a sacred character that goes far beyond what constitutions in other places get. This sacralization is in many way unrelated to the practical content of the document as a set of basic rules for a government. Sure, the 1st, 4th, 5th amendments are good ideas, the 3rd is downright obsolete, and the 2nd is contentious. But because the rules are all we got, they become a focal point for coordination, and pointing out that the words on the page might be confused, or obsolete, or unrelated to how we employ them today, is considered gauche.

Is it dangerous to point out? Not more nor less than other forms of critical theory. Is widespread knowledge of Foucault dangerous for the legitimacy of psychiatry, of Judith Butler for gendered norms? Kinda, but those institutions are functionally robust in other ways. The Psmiths are riding the coattails of the entirety of sociology and political science here.  I would flip the causal arrow: in most cases, dissatisfaction with existing institutions leverages critical theory to attack them. But the failure of existing institutions causes the unrest, not critical theory itself.