(x and y => z) does not contradict (!x => z)
Instead (x and y => z) implies (!z => !x OR
!y). If you theorize that (!x => z) then (!z => !y). In this case, the Fed existence and increasing the money supply would lead, in theory, to a less severe Great Depression. Friedman also theorized that if the Fed didn't exist, other sources of liquidity would have appeared to mitigate the depression. Given the Great Depression was severe (ahem, its called the Great Depression), then, it must be the case the Fed fell down on its job. No contradiction here.
Lot's of people get logic wrong. I just wish Paul Krugman didn't