Even the finest pilots in the world, when suddenly presented with a simple failure (double engine failure, for example), will sit there and think "no - this can't be happening" followed by "what on earth do I do".
Half right in the case of Cactus 1549. 'The physiological reaction was strong and I had to use training to force calm on the situation. I was sure I could do it' said Capt Sullenberger.
The 'finest pilots in the world' are probably amongst the best trained pilots in the world. Good training undoubtedly makes a difference to outcomes.