Am I committing the ratio fallacy when I calculate the Pearson's correlation between a variable x/y and a variable z, with no common terms?

I have found a similar question to mine here but the reader is referenced to a paper goes far beyond my understanding: "Spurious Correlation and the Fallacy of the Ratio Standard Revisited" by Richard Kronmal (1993) Journal of the Royal Statistical Society. Series A (vol 156, no 3, pp. 379-392).