They didn't know the trapezoidal rule.
The point is that the "because the investigators were unable to cite an unpublished work, I submitted it for publication at their request" justification doesn't make much sense. She could have just explained to them that no citation was needed for something so trivial.
I can see how if you were unaware, and several colleagues in your field were unaware, it might be good to include some kind of external information about the thing. I can also see why you might not want to link to Wikipedia.
I do think writing a medical article about it for people to link to is silly. Surely if you wanted a citation, you could just cite a math textbook.
Aren't many Nobel Prizes in Economics done like that? Take some well-known math/physics formula, rename variables to make them represent some economic quantities, name the resulting formula after oneself, publish, get the prize?
You cannot trivialize this step. Most people's job in data analysis is basically this. Figuring out what quantity fits where in the formula _is_ the research.
edit: To make it clear, it would have been fine if here model explained something using trapezoidal formula. But she seems to be claiming the formula, not a model.
She didn't name it after herself, the users did:
> collegues ... began using it and addressed it as "Tai's formula"
As is typically the way with eponymous scientific works, people citing the work add the author's name e.g. Maxwell's equations or Higgs' boson. The author doesn't typically declare "I have discovered X, which I shall call ${self.name}"
[1] (PDF link https://math.berkeley.edu/~ehallman/math1B/TaisMethod.pdf
I don't think this rule applies here, because the paper introducing "Tai's rule" calls it "Tai's rule" rather than others citing it. As if Higgs called it Higgs' boson in his paper.