The division of labour on the Saturn Vs construction proved, in retrospect, to be a double-edged sword. On the one hand, it allowed the rocket to be completed at an incredible rate, certainly responsible for the success of the Apollo program.
But on the other hand, building the rocket at such a rate and with so many subcontractors means the people who oversaw and understood the actual assembly and overall working of the Saturn V were few. Each contractor recorded the workings of their stage and records survive about the engines used, but only a handful of engineers from the MSC knew how Saturn V puzzle fit together.
It is possible to work backwards to recreate individual aspects of the technology, but the men who knew how the whole vehicle worked are gone. No one alive today is able to recreate the Saturn V as it was.
Worse is the lack of records. Without a planned used for the Saturn V after Apollo, most of the comprehensive records of the rockets inner workings stayed with the engineers. Any plans or documents explaining the inner workings of the completed rocket that remain are possibly living in someones basement, unknown and lost in a pile of a relatives old work papers.
Two Saturn Vs remain today as museum pieces, but it is likely that the rocket will never see a rebirth and reuse in manned spaceflight.
Yes, NASA put men on the moon with 1960s technology, but that technology doesnt exist anymore. By default, neither does the possibility of a manned lunar or Martian mission for that matter without a new launch vehicle. A new heavy lifting vehicle will eventually come about it will have to for NASA to pursue its longer-term goals. Until then, NASA is bound to low Earth orbit and minimal interplanetary unmanned spacecraft.