If you had said that being bailed out would not be some players cup of tea, I wouldn't have responded to you. But it was only because you had made a seemingly universal declaration (which I had quoted) that I felt the impetus to reply somewhat cheekily.
That being said, I agree with you. Some people
would find it to be a betrayal of the game and the ethos of playing it-- no argument there. But we do have to acknowledge that it isn't a universal response and that there will be plenty of tables wherein a DMing copping to a mess up (especially if it's the first time of it ever happening) would be seen as graciousness and concern for the enjoyment of the players.