That is one of those completely inane statements on several levels. There is more total GDP and higher levels of GDP per capita in every country with a strong central bank now than there was before those countries had strong central banks. Before we had central banks intervening in economies we had things like the great depression, and before we had central banks at all we had things like the dark ages. So first it's simply objectively false to assert "It has been documented in 100% of cases that their actions only make matters worse." Where exactly has this been documented and by whom?It has been documented in 100% of cases that their actions only make matters worse. Good luck.
And second, this type of statement is absurd in the same way as it would be to claim since someone died 2 years after treatment for cancer the doctor must have made the cancer worse. The fact that recessions have happened despite central bank intervention in no way "proves" that the banks even failed, let alone that they "make matters worse". You would need a control without central bank intervention to know that, and absent that a basic understanding of macro to see what would have happened absent the intervention to at least be able to talk intelligently about it.