All that means is that you don't have to point to the Constitution to prove a right exists. The right still has to exist somewhere and be recognized.[1] The power of courts to access nearly all evidence with due process predates the Constitution and nothing about that document shows any intention to alter that practice.
[1] "Rights" are exceptions, not the rule. The rule is the will of democratically elected legislatures. Rights are exceptions to democracy and should be construed to swallow the rule.
Rights are expansive. There is no "precautionary principle" when it comes to rights. If a new thing is discovered, like strong encryption, I have a right to use it in conjunction with my other rights. If I can make a cheap personal rocket, I have a right to launch myself into orbit, as long as I'm not infringing on others' rights. The fact that such a rocket means anyone can build an ICBM doesn't put it outside of one's rights.
Governments have no inherent power to "inspect." You seem to think governments should have superior powers to individuals. While there is a philosophical argument for this, that doesn't mean it's always going to be true.
It's fallacious to use the concept of "enumerated powers" and "limited government" to argue that "rights" in the U.S. are, or were intended to be, structured the way you describe. "Limited government" concerns the allocation of power between the state and federal governments, not the relationship between those governments and individuals.
State governments are not ones of enumerated powers and they are not limited. They are successors to the British Parliament and inherited the powers of that institution including the general police power. Against that backdrop, "rights" are those specific restrictions on the exercise of that power that states have bound themselves to by the federal Constitution and their own constitutions. There is no room in that framework for an expansive conception of rights that all exist so long as you're "not infringing on others' rights."
A great concrete example is blue laws, which were widespread at the time of the founding and regulated everything from alcohol sales to food consumption. Some of those have been challenged, hundreds of years later and mostly unsuccessfully, on establishment clause grounds, but there is little doubt the states, as a general principle, have the right to regulate public morals.
Enumerated powers of government. Unenumerated rights of the people.