Upon closer examination, that appears to be the business end of a Saturn IV, which is a good deal smaller than a Saturn V. The covers on the thrust nozzles are not usually present on museum pieces. Neither had been fired prior to 1961, so this may be an assembly building at Marshall.
The point I want to make is the Saturn boosters were being developed before the media gave all the credit for the Moon program to JFK. Work on the F1 engine also began in the mid 1950’s.
http://en.wikipedia.org/wiki/Rocketdyne_F-1