No, it means that the role will exist forever at that company, as far as anyone knows. It means the company has no plans to ever eliminate it. You may die or quit, but then someone else will be hired to do that job.
Except permanent jobs are frequently made redundant and cease to exist. The original intention may have been for the job to exist forever but things change, and permanent things cease to be so permanent. Much like countries...
As I wrote above, it means that the role is permanent as far as anyone knows. It does not mean that you will permanently be doing that job. It means that, based on all available current information, the job will continue to exist forever.
Of course, people can and do make mistakes. The fact that someone chooses to use a word to describe something does not mean that it's necessarily an accurate description. They may be lying, or they may simply have judged the situation incorrectly. How many startups say "we are the next Google"?
So then, using your logic, the governments of East Germany and the Soviet Union would, at the time, have been considered permanent, as those governments were expected to last forever as far as anyone knew.