It will affect the price of bitcoin because it is basing the value of it to dollars. And most of the currencies all around the world are basing to the economy of US, so when there is a crash to US. Most of the economy for each country will also fall. I don't know why US is this too much superior when it comes to financial things.
Not quit true that if US economy fall all the economy outside US will fall, same way the price value of bitcoin wont be affected by crash of USD insted the price value of bitcoin in USD will only be affected, because outside USD bitcoin price have relation to other currency. IF USD fall the price value of bitcoin is still the same in relation to other currency but USD.