This is a story of how one became better golf player by increasing his strength: https://www.youtube.com/watch?v=sr2pgBTRpK4

One can enhance cognitive functions by strength training: https://pmc.ncbi.nlm.nih.gov/articles/PMC8534220/

Aside from time travel, the best way to improve in very important things is through strength training.

The saying isn't "The only way..." but "The best way...". Of course one may improve with all the things you mention, and it's a tongue-in-cheek statement anyway, but there's a grain of truth to it. I saw it quoted by one of the greatest teachers in golf, Harvey Penick.