> As a trivial example, a stock whose price started at $1 and increased by $1 every day for 30 years would span 4 orders of magnitude over that time period, but would not follow Benford's law.
That's actually a great illustration of the kind of thing we'd expect Benford's Law to raise red flags about. Your hypothetical posits the kind of behavior that we would not expect to naturally come out of the kind of process that governs stock prices over time. Stocks simply don't have their price go up by exactly one dollar a day, every day, for thirty years.
(This is briefly covered in the the article, which describes how the other big assumption of Benford's Law is that you're working with a system where things tend to change by percentages rather than absolute values. So yeah, it's true, covering orders of magnitude is not sufficient. Nor did I claim that it is, mind. I was just pointing out the assumption that I thought he original poster was missing.)
So, if we saw the kinds of initial digits that your hypothetical produces, we would be correct to guess that this stock is behaving in an unusual way. And it would be a correct application of Benford's Law, because we can reasonably expect that its key assumptions apply.
By contrast, if we hypothesize a stock whose price goes up by exactly 0.0001% every day for 30 years, its record of daily closing prices would obey Benford's Law. In fact, it would match it so well that we would also (correctly) consider it to be suspicious.
No, it's not a formal justification in any case. It is just a red flag. It turns out that red flags are useful even when they're not admissible in court, because they provide an easy heuristic that you can use to help direct your search for more compelling evidence.