This paper evaluates the significant historical paper of Muller and Mott-Smith (1930), which successfully disputed the proposal of Olson and Lewis (1928) that background ionizing radiation is the driving mechanism of evolution. While the present analysis supports the general conclusion that background radiation is not a quantifiable factor affecting evolution, the paper reveals methodological errors and questionable conclusions in the Muller and Mott-Smith (1930) paper, which may have impacted the acceptance of the linear non-threshold (LNT) model. Most importantly, this paper reveals that in Muller’s (1927) Nobel Prize research he used a treatment exposure (total dose) that was 95 million-fold greater than the average background exposure, a value far greater than the 200,000 fold reported by Muller and Mott-Smith (1930). Such a large exposure rate discrepancy may be historically important as it may have led to the over-reliance on Muller's research in support of the derivation and use of the LNT single-hit model.