You don't base an assumption off of just 1 metric, there should be more information as to what the people did, especially with such a small sample size....
Believe what you want, but I think you have a very misguided view of statistics.
Given that you do not know the difference between "majority" and "plurality," you might want to refrain from making statements that you can't actually back up.
Also, how is this a small sample size? It may be a biased sample in certain aspects, but it isn't small, not in the way you are suggesting.
In the real world, getting more detailed data is often an unaffordable luxury. We have several variables that are either impractical to gather or simply unavailable to us (i.e. whether Nintendo is holding off on banning some people but not others). However, of the people who have been banned, the overwhelming majority have been sharing their data with Nintendo. Given that this is a plausible way that Nintendo could detect illegitimate usage, it is safe to make a tentative conclusion that this is a likely cause of the bans, despite not knowing all of the details. It doesn't mean that this is the only cause, just that it is a common vector.