I kind of view this as a bit of a problem: If it is so, presumably they have orders of magnitude more capacity for control and amendment and could have very plausibly been editing every last bit of digital data we've relied upon over the last 70+ years. They could well have been re-writing our entire view of the universe.
We need an order of Analogue Eternally-watching Monks we rely upon to fact-check basic assumptions using entirely non-digital means. Which could get complicated.