Those numbers are fiction. Government was engaged in massive price fixing during the entire New Deal and WWII period. GDP is compiled by aggregating quantities sold and prices, but the prices weren't real market prices. They were bureaucrat dictated prices.
Also, incredibly, the GDP calculation counts government spending as production when it is obviously consumption. Back the public sector portion of GDP out twice (once because it shouldn't have been added and once more because it should have been subtracted) to get a better picture of what the economy was doing. (Though even this won't make the GDP numbers from the FDR period reliable.)
Which numbers? Can it be doubted that there was a substantial contraction between October 1929 and March 1933?
My point is that just about anyone could have presided over a "recovery" following such a massive contraction, not that the post-1933 numbers are 100% accurate.
We do not need to make these things up...