I can see the merits of this argument. However, I feel that people should have at least a basic understanding of what they are doing when it comes to mathematics. My reasoning for this is simply that if you try to introduce people who are trained as such to new and more complex issues mathematically speaking, then they are very likely to fail in a large fashion. With technologies advancing as fast as they do in these fields, these people need to have the latest tools available to them to ensure their job safety, and when these tools are mathematical it is essential to have at least a basic understanding of the principles behind them in order to use them to their full potential.
Whether you agree with my viewpoint or not, this is my opinion