How is someone supposed to prove that in a specific case? It would be the case for a company that failed by a specific margin whose total borrowing costs were increased by more than that margin. Which requires speculating what their share price would have been in the alternative, calculating the resulting effect on their contemporary borrowing cost (which data is available where?), then evaluating their entire business to determine how much additional capital they would have needed to survive.
It would take hours to calculate and be subject to unlimited debate about the reasons and margins by which they failed.
But if you really want an example based on pure speculation, Kodak. They made their share of mistakes but if it had been easier for them to raise funding to compete in digital markets once they changed course they might not have ended in bankruptcy.
And I still haven't heard any argument as to the flaw in the general principle.