Ted Hill's papers on Bedford's law are from 1995, and this chapter is from 1997. Wolfram's date is incorrect, although the secondary phenomona that choosing from a distribution which itself was chosen at random is log normal was proved at that later time.
The 'straw-man' was misunderstood by you. The author points out in the conclusion of that paragraph that all of these pseudo-scientific or grandiose explanations where nonsense.
The 'proof' is really an explanation that the phenomena presents itself to an easier analysis when viewed in terms of FTs. The computer program is there to show the reader the 'repeatedly divide by ten' action which is implicitly going on when we map from the unbounded domain to a small bounded domain.
Its a nice explanation really, but as the problem was solved years earlier and this analysis isn't given with another application, I can see why it wasn't accepted for publication in a pure math journal.