It's actually very true. The
Tenth Amendment establishes that "The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people." This means that the federal government here only has the power to do things our Constitution says it has the right to do. Everything else is managed by the states. This is why when you become a lawyer, you pass the state bar (unless you're specifically becoming a federal lawyer); almost all cases are tried at the state level, not the federal level, and each state has its own set of laws (though many of them end up being similar).
There is the concept of
incorporation, though, where certain federal-level laws are applied to the states, specifically those in the Bill of Rights. What this means in effect is that the states can't infringe on rights guaranteed by the Constitution; Wisconsin, for example, can't make a law that restricts free speech even though the right to free speech is only guaranteed at the federal level.
I think the idea of local control over governance is a good idea that has in some ways been executed poorly. I think giving people more of a say over their own affairs at a local level and only delegating certain powers to the federal government (such as the power to guarantee certain basic, universal human rights) is the right way to set up a democratic government.
A real life example that comes to mind is the gas-powered car industry versus the electric car industry. In a situation with strong federal power, the entrenched traditional cars industry could make laws that affect the entire country that prevent the sales of electric cars at car dealerships, whereas in our system, they can only pass such laws in individual states. This has actually happened and in certain auto industry-friendly states, companies like Tesla can't sell their cars at dealerships because the auto industry was able to get laws passed that blocked it. However, in states like California, where Tesla is bringing in a lot of money and has a lot of popular support, they can't pass these kinds of laws. Our system enables companies like Telsa to get off the ground even if a powerful industry has an undue amount of influence in most other places.