I think that's a reasonable historical interpretation of the 14th Amendment, but not one that currently holds weight even from the most conservative justices on the Supreme Court. Whether rightly or wrongly, the Supreme Court has taken an expansive view of the power of the 14th Amendment. In the end, federal courts always trump state courts in areas where they share jurisdiction so we have to live with the federal interpretation. Don't like it? Get better judges.
The response at this point is state nullification of unconstitutional federal acts and decisions (possibly followed by the long shot of a successful Article V Convention of States that somehow forces the unconstitutional portion of the federal government (my estimate=about 80%) to shut down - not likely to happen).
The problem is the totalitarian federal government which has completely loosed from the Constitution. The solution to restore freedom and limited government is restoration of the Constitution. The states are the battleground for the preservation of the Constitution IMO.