But what if the researches themselves are part of the conspiracy?/s
My prediction is that within six months you will a Flat Earth moderator- a most excellent response. Well done and bravo!
Rude.
But anyway, on the OP, it's not the best example. It's entirely possible to claim the conspiracies that were the source of the data are in fact outliers: we obviously don't know anything about successful conspiracies, or how long they last.
Plus it depends on the model. The conspiracy can be minimized, or compartmentalized. For example, if NASA are faking space travel, they wouldn't necessarily know ESA are too: and it's possible to have unwitting helpers. I remember seeing one person make the argument that the civilians who've been to space still think space travel's fine and possible, there are just insurance issues or something with bringing them up: NASA or whichever agency's responsible just give them a few trick photos to show their friends and family etc.
All depends on the model you're arguing against. Extreme conspiracy theorists would call the data based on outliers and so unreliable: more minor ones would actually have a fairly minimal conspiracy.