For reasons explained in the article, we are bad at estimating small probabilities.
Similarly, we are bad at estimating small proportions ("easily shave 2%"). What is being claimed in the parentheses here is that there's a probability distribution of "how much costs are shaved" and that we can estimate where the bulk of its support is.
But we're not really good at making such estimates. Maybe there is some probability mass around 2%, but the bulk is around 0.5%. It seems like that's a small difference (just 1.5%!) but it's a factor of 4 in terms of savings.
So now we have a large number (annual spend), multiplied by a very uncertain number (cost shave, with poor experimental support), leading to a very uncertain outcome in terms of savings.
And it can be that, in reality, the costs of changing service turn out to overwhelm this outcome.
When modern advertising is a spectrum of “lies, damn lies, and statistics,” I don’t blame folks for crying foul and demanding a baseline level of truth in advertising. When folks trust but verify, this is seen as a change in the status quo by folks, and some of those folks who protest about it in those terms are trying to sell you something.
