So you’re quibbling with meaning 1 over meaning 3.
Both are legitimate uses of the word by your own source.
Definition of FERTILE
1 a : producing or bearing fruit in great quantities : productive
1 b : characterized by great resourcefulness of thought or imagination : inventive (a fertile mind)
1 c obsolete : plentiful
2 a (1) : capable of sustaining abundant plant growth (fertile soil) (2) : affording abundant possibilities for growth or development
2 b : capable of growing or developing
2 c (1) : capable of producing fruit (2) of an anther : containing pollen (3) : developing spores or spore-bearing organs
2 d : capable of breeding or reproducing
3: capable of being converted into fissionable material (fertile uranium 238) — fer·tile·ly adverb — fer·tile·ness noun
I made myself very clear as to why I thought birthrate was a conflation of the term fertility, so I really shouldn't need to explain that further.