For me, it was the thing about the article I found most interesting!
I'm not sure Barendregt is claiming to have invented it, and in your quote, Smullyan doesn't either. I've only skimmed the paper, but the paper is framed as an introduction to the λ-calculus and SKI-combinators, not as a presentation of novel results in the field. Its section "0. Preliminaries" (♥) does claim to present a novel representation of recursive functions, but doesn't bother to mention the numerals. In a journal paper published today, the absence of an endnote there would amount to a claim that the representation of numerals was novel, but I don't think that was necessarily true in that less-bibliometrics-plagued time. Though Barendregt does cite 18 sources in his endnotes, so maybe so.
I'm not sure Barendregt is claiming to have invented it, and in your quote, Smullyan doesn't either. I've only skimmed the paper, but the paper is framed as an introduction to the λ-calculus and SKI-combinators, not as a presentation of novel results in the field. Its section "0. Preliminaries" (♥) does claim to present a novel representation of recursive functions, but doesn't bother to mention the numerals. In a journal paper published today, the absence of an endnote there would amount to a claim that the representation of numerals was novel, but I don't think that was necessarily true in that less-bibliometrics-plagued time. Though Barendregt does cite 18 sources in his endnotes, so maybe so.