Yes.
It's reasonable to assume that any somewhat socially competent person doesn't relish the idea of letting people go.
That should be a given.
And taking responsibility is just restating the fact that the CEO has all the power while (in this case) nothing the individual employee could do would have prevented it.
The CEO did not fire himself for failing and is (probably) still wealthy and doesn't need to potentially uproot his life.
"Sorry" doesn't buy you anything.