Conspiracy theorist thinking allows you to take it one further in the case of discredited/debunked stuff. All you gotta do is add another layer to the conspiracy. Real conspiracy theories regularly do this to try and wrangle out of being debunked, but it serves fictional needs even better.
Like, IRL we now know the face on Mars isn't an actual thing, but it'd be simple to suggest in-game that it WAS real, and the Mi-Go destroyed it after the Viking photos became public.
Or: crop circles are known fakes... except these particular ones are someone using the general hoaxing as a steganography cover.
Or: the reason no-one has been able to find any bigfoots/skunk-apes/yeti is because they're hollow earth dwellers, and the only times we see one is because that one accidentally stumbled on a connecting cave and had a Lovecraftian experience of his/her own on the mythical "outside".
Or: the hollow Earth actually a D-brane cyst anchored to the earth's gravity well, not an actual geologic hollow (this is actually the explanation for R'lyeh I've always favored, which I'm repurposing here for hollow earth). You'd need a lot of collated relativistic measurements to detect it, so without intervention humanity wouldn't be able to discover it on their own until interplanetary travel became common.
OK, so those last two weren't conspiracy theories, but the same "add another layer" principle applies.