This equivalence seems impossible. Let me explain, and then someone smarter than I am can say why I'm wrong.
The tangency portfolio is defined by risk and returns, whereas the market portfolio is based only on market caps. Current market caps contain NO INFORMATION about historical risk and returns. So how can they give the same result?
For example, consider an alternative universe where I replace certain stocks with versions having half their rate of return, but correspondingly longer history so that the market caps today are the same. I don't need a calculator to see that the efficient frontier will be different in this alternate universe. But the market portfolio will be the same.
We can cook up similar examples for modifying volatility. In any case, it appears that we can dramatically alter the risk and returns of our assets while maintaining current market caps.
What I do believe is the EMH, if tangency is optimal and all investors flock to this same portfolio, then the market will BECOME the tangency. But that is a very different claim than simply tangency = market.