Actually I don't think this is true. In a recession, btc could easily go up in nominal or even real value. If they are simply treated as an investment, and not a currency, then you could have people selling off bitcoins in a recession because they feel its a risky investment, and their confidence is down. This would drive down the value of bitcoins.
But, if bitcoin acts as a true currency, we could easily see the opposite effect in a recession. Particularly in the case of a US default, which would cause massive capital flight and tank the value of US currency, and raise the value of all other currencies. Particularly if the bitcoin is seen as a safe currency, it could substantially rise in value in the case of a recession. It could go either way.