The bosses in the typical quant firm are also quants themselves, and have no trouble following the rigor used to justify the validity of a trading strategy. Sure, at a certain point in the chain, you're talking with someone (eg. COO) who isn't allowed to see the details of the modeling procedure, but this is the point of scaling up and having risk/pnl limits -- no HFT firm, for example, is at risk of blowing out from lack of statistical rigor.
I doubt taking Yale's financial markets courses is sufficient to understand or be exposed to what is currently being used in quantitative finance. I took Stanford's financial markets and statistics classes, and those are far behind and unaware of what's currently being used in the industry (I've worked in two highly successful HFT groups since Stanford).