I think the question has been finally answered on did they really mean exactly 200 years or roughly 200 years (say 2004 years) per Todd Howard "Fallout 4 is set mostly after Fallout 3."
Some people may still be floating on the Nile, but having Fallout 4 start 2 months after Fallout 3 started is mostly after.
Having Fallout 4 start 4 years after Fallout 3 is not mostly after.
It is after the events of Fallout 3.
See for yourself:
Fallout 4 interview: Bethesda's Todd Howard on building the apocalypse - July 7th 2015
http://www.telegraph.co.uk/technology/video-games/11723096/Fallout-4-interview-Bethesdas-Todd-Howard-on-building-the-apocalypse.html