Data Science is still approachable through the "Edison"-style: only do as much math as your comfortable with, but keep probing discrepancies between different models. It's more debugging than architect-ing.
Evidence: none of the top kaggle competitors is an academic/statistician to my knowledge.
I understand what you are saying, and I am not looking to become a mathematician or statistician. It has just been so long since I took a math class that before diving into any of these courses, I'd like to be aware of the minimal fluency expected.