Shortages without printing would not lead to inflation - it would lead to substitution. All inflation is ultimately caused by the Gov (name the famous economist that said this  )

And I agree that the Fed does not control long term interest rates....until you start with YCC...massive QE.  Even then it's questionable because the numbers get so big. That's why every bail out is magnitudes larger than the last...because we print to get out instead of solving the underlying issues....then the next time we have reset price levels and have to print even more to have the same effects.