What if the bag of paper "money" is in a foreign currency? You'd still happily call it money, but then the distinctions you're trying to draw with crypto don't really apply. Think of crypto as a foreign currency, it still functions as money.
Crypto isn't foreign currency. The price may fluctuate wildly based on sentiment and action taken by exchanges such as Binance, which would directly impact their obligation here.
Comparing crypto to actual currency typically connected to large, real economies is not relevant here.