Nope. If real money has to be paper money then you are mistaken. Fiat currency is by no means "real money". It is based on the trust in the government, and if that trust dwindles then so does the currency the government prints.
Bitcoin in my opinion is real money, and gold and silver was real money. Real money is a concept that evolves through time. It's not something that is always the same.
In this respect Bitcoin is no different from fiat
Its value is also based on something ephemeral like the trust of people in the government. Namely, that people will continue to use Bitcoin in the future and won't abandon it in favor of some other currency. That trust is also quite volatile which could be easily seen through price fluctuations. When the Bitcoin price increases, so does the trust in Bitcoin and vice versa. Only precious metals cut it somewhat as real money inasmuch as you understand it