I do not know if that saying is true, but I can attest that since becoming employed the few jobs I have inquired about were interested in me. Whether that is simply the right people looking at my credentials instead of the wrong people, I am not sure.
The idea behind needing a job to get a new job is that people who are employed are doing something right. Employed people are not crazy enough to be fired. Employed people are currently valuable to some company. Employed people, engineers and scientists in particular, are staying current with new developments in the field, which will allow them to make better products and cut costs. Employed people are not lazy. I have no idea if anyone actually things that last sentence, but I always had a hard time describing what I did while I was unemployed. I applied for jobs. That was kind of a big part of most of my days.
For people who have recently graduated into unemployment this is a catch-22. You need experience to get experience. On the upside, our time in life is the one thing that everyone shares. Billionaires aren't awarded more of it than poor people. Which is to say, all of life is an experience. Work experience may be valued by an employer more than unemployment experience, but they are not interchangeable. The experience I had unemployed will probably stay with me the rest of my life and help me far more in the future than one year of engineering. That being said, now I have a contract engineering job, so I hope that experience will help get me a long term job.