Modification or not, I asked that you provide an authoritative citation or at least an example where this occurred. In contrast, I can provide a large number of counter-examples where it was not true. You can start with this list:
ACTS OF CONGRESS HELD UNCONSTITUTIONAL
Not all of those will apply. In some of them, the district court held something unconstitutional, but the circuit court disagreed, and then the Supreme Court agreed (with the district court). In others, it was the district court that got it wrong first, and the circuit court was the first to agree that it was unconstitutional.
A US district court decision does not automatically change the law in the entire US. It certainly calls things into question, but it's not even a binding precedent outside that district.
Revoking a law nationwide requires a decision by the Supreme Court, although you can achieve the same thing with a Circuit Court case that becomes precedent nationwide. That's why the Supreme Court rarely takes a case unless the Circuit Courts disagree -- there's no need.
It'd be nice if that were a declarative statement. For example, amending the First Amendment to read "Congress shall make no law."