The standard biographical source reports Dodson's rejection-to-design causation as hearsay — 'It was said' — and no located source has Dodson framing it that way himself

The question was whether James Dodson explicitly framed his 1756 age-scaled premium scheme as a response to his own rejection by the Amicable Society, or whether that causal story is a later tidying. The Oxford Dictionary of National Biography — which the question named as a resolution path — answers it in its own hedge: "It was said that he was denied admission to the Amicable Life Assurance Society, being over forty-five years old, and that this led him to advertise asking for those interested in a project for a new form of life assurance to meet him at the Queen's Head, Paternoster Row, on 2 March 1756."

Two things follow. First, the ODNB does carry the causal story, so it is not an invention of popular retelling — it is in the standard scholarly biographical reference. Second, and decisively for this question, the ODNB marks it as report. "It was said" is the phrasing a careful biographer uses for a tradition they are passing on rather than a fact they are asserting, and the entry offers no source for it, while sourcing the surrounding chronology precisely.

The chain closes on itself in a way that matters. The ODNB entry's own first-listed source is Ogborn's Equitable Assurances (1962) — the very book this vault held for years as the strongest lead on the causation. So the standard biography, having read Ogborn, reports the causation as hearsay. That substantially reduces the expected yield of reading Ogborn directly: whatever he says, it did not persuade his most careful reader to state the causal link as fact.

Corroboration from the other direction, and freely available: the Journal of the Institute of Actuaries review of Ogborn summarizes his account of why life assurance arrived when it did, and gives four causes — "the climate was favourable, England was prosperous; the mathematics of life contingencies was at hand; and there was an unsatisfied demand" — plus a fifth: "It also came when it did because one man, James Dodson, F.R.S., was determined that it should... He conceived the vision of a mutual life assurance society conducted on scientific lines." The word "Amicable" does not appear anywhere in the review — which runs pp. 387–389, about two and a half pages, signed A. H. Rowell — nor anywhere else in the seven-page Reviews section (pp. 387–393) that carries it. That the silence spans two and a half pages rather than seven is a narrower base than this note first recorded, and the argument from silence should be weighed at that length. Ogborn's explanation of Dodson's motivation, as his reviewer renders it, is vision and mathematical capability — not exclusion.

The primary route the question hoped for is also closed, and this is worth recording because it was the plan of record: Dodson's First Lecture on Insurances is, per the ODNB, unpublished. It cannot be consulted for a motive statement without archival work on the manuscript.

So the honest state is: the rejection is well attested, the design is well attested, the causal link between them is reported tradition. The vault's Dodson note should carry it as such, and the "excluded → rebuilt the system that excluded him" shape should be read as a story the sources repeat rather than one they document. The negative half here is an argument from silence over two summaries of Ogborn rather than over Ogborn himself, which is a real limit (moc-argument-from-silence) — but the silence sits in exactly the place a causal claim would have to appear, in a reviewer's summary of the author's own account of causes.