Is the Darwinistic Selection Principle False?

No that is not what Darwin says AT ALL.
Selection is just about viable progeny. If intelligent people decide to have no children then they shall not pass on that trait. If stupid people breed like rabbits, and the leads to viable progeny, then it is THEY that get to pass on their traits.
It is not rocket science.
During the last 120,000 years when anatomically modern humans energed from Africa it took intelligence to compete against Neanderthals, and to master the wild, build weapons and shelters and to colonise the whole world.
During those times it was only the smartest that could survive. Intelligence was selected because stupidity usually meant death and not reproductive success. These days, at least in the West, there are few pressures as there were before, and family planning is now a choice whereas before it never had been.
But what Darwin said stays- no matter what traits you have it is reproductive success ONLY that drives evolution.