Not true at all. I know multiple people who have overcome training failures (121 and 61), aircraft incidents/accidents, or arrests and made it to majors. It isn't a test of "how much you can f up and make it a major", we all fail at different points in life. It's how we overcome those failures that define us. We as a society are (should be?) progressive and if you can prove that you grew and are a better person or employee from a negative experience then you will certainly get the green light. Undoubtedly, it will be more difficult than the pilot who has a perfect record and good attitude but it is by no means impossible to move on.