The figures could be still be reliable if this reflects an actual change in distribution of business.
Speculation: Perhaps in 1960 businesses were really distributed according to a power law but have reapportioned a bit over time. Trends like consolidation and dominance of a few large firms might skew things.
As a soon to be CPA, these recent articles on Benford's Law fascinating. But it's funny that there's extreme skepticism around Moore's Law, but Benford's Law seems to get a free pass. Just like Moore's Law it's a law matched to empirical observations - meaning it works until it doesn't.
Auditor, and very soon to be CPA, here. The author "downloaded quarterly accounting data for all firms in Compustat, the most widely-used dataset in corporate finance that contains data on over 20,000 firms from SEC filings." Quarterly reports are unaudited by an independent CPA firm (most often KPMG, PWC, EY, Deloitte), while annual reports (10-K) are audited. I would be curious if the the sum of squares analysis is as significant in the latter set.