Perfectly true - which is why you must do everything possible to ensure that you are part of the redundancy process (assuming you've found that next job). That way you win both ways. Maintain a low profile on the success of your job hunt.
Don't forget the the employer must give you reasonable time off when under notice of redundancy to find alternative work- decent employers will be offering career-counselling anyway as part of exit strategy.
You will probably be okay if you wait until redundancy notice has been served before you accept the other job. But bear in mind that occasionally ask people to stay on a bit longer or find an alternative role- I know people who were told on their last week that they would be required to stay on for a period. If you refuse because you have another job you could lose your severance pay