My experience: I had basically zero math background, but I took ML with Ng and probabilistic graphical models with Koller, and later was a TA for Ng's ML class, during my Masters' degree and thought I was all set to go into machine learning jobs. To my surprise, I consistently found myself in interviews stumped by questions from basic stats, particularly significance testing, which people with more traditional stats backgrounds assume is basic knowledge (and it should be), but which wasn't taught in any of my ML classes.
I'm in a job now that involves some machine learning, but the ML component is 50% marshalling data (formatting, cleaning, moving), 40% trying to figure out how to get enough validated training examples, and 10% thinking about the right classifier to use (which someone else already implemented). Which to be honest is not very interesting.
So yeah, becoming a real data scientist is hard, requires a lot more knowledge than you get in one ML course, even from Andrew Ng, and the reality of the work often doesn't make it some dream career. And the competition for jobs isn't from other people who also just took that course -- it's from PhD statisticians and statistical physicists who might have taken one ML class to show them how to use all the mathematical tools they already have to do the new hot thing called machine learning.