The transactions can just be recorded in this SQL database, and the "reserve" would be untouched. If someone wants to exchange their BTC to USD or Euro, they can go to a money changer, their SQL database entry will be decreased, the money changer's SQL database entry will be incremented, and the total BTC in the reserve remains.
Hmm, I think I just described the so-called Lightning Network, which means in the end you have to trust a central authority after all. (EDIT: After reading about LN, it seems this isn't how the Lightning Network works).
They might as well make something like "El-Salvador-Coin" without needing dumb blockchain stuff.