Conspiracies are often true.
Conspiracy theories are generally false.
Many popular conspiracy theories involve huge numbers of conspirators - thousands, or even hundreds of thousands. For anyone who has a "feel" for how math works, it seems wrong. Putting some hard statistics work around it makes the false nature of large-scale conspiracies more concrete for those of us who believe in math.
A conspiracy theory where no more than a dozen people need to be involved makes sense to me. A conspiracy theory involving every climate scientist in the world, or every doctor in the world, or every NASA employee, seems like BS.