I think one should always strive to be modest in both victory and defeat. Spitz could have easily said less and have appeared magnanimous.
There's an American chap called Michael Johnson who set a couple of World records for running rather quickly. He's been commentating on the BBC and a more modest fellow would be hard to find - he was delighted that the Jamaican chappie beat his records and heartily congratulated him. He did not compare himself other than saying that the Jamaican was the better athlete.
That's sportsmanship rather than brinkmanship.
Time for another doughnut. It's my birthday today! :cheers