He's right that with zero interest elasticity, the Fed could still expand the money supply. Just think of the old helicopter drop.
However, I do not think that Bryan's personal money demand function is the ultimate determinant of interest elasticity.
The Fed supplies bank reserves. Mechanically, it goes into the "repo" market, which is the market for loans collateralized by Treasury securities. When the Fed wants to expand the money supply, it goes long in the repo market (meaning that it makes more loans), which lowers the interest rate in the repo market. So as a practical matter, the interest rate goes down whether Bryan adjusts his money demand or not.
The repo market, unlike Bryan, gets very exercised over tiny changes in interest rates.