While most groups worth with teams, some generalization in all members is a good idea. Everyone should have basic mathematical knowledge, otherwise they are going to waste the time of the math & stats experts, as well as their own, with stupid questions and requests (everyone I worked with had that problem with our local math dunce). We'd answer some odd question, the person would go back, do something, ask more question, and halfway through we'd finally find out what they were spending so much time on, and realize how bass ackward they were going about it.
to put it in your terms, it'd be like someone doing the 3D programming and not knowing much about trig or vector math. There are libraries around that would would do the grunt work for them, but they are still going to cause problems. Math and stats are integrated into every aspect of science.
However, at the same time you can't specialize in everything, and almost everything is done in a team these days, so having specialists with different topics is better than having everyone be a generalist, so long as you can communicate and work together. Where I am now, a very large number of research teams have statisticians on board for that very reason - a lot of scientists are more familiar with their specific fields than the nuances and tools of statistics.