the version I learnt the phrase from had the end of the chain as
- oh we should paint it
- we need a paintbrush
- I hear yak hair makes the best paintbrushes
- here I am, shaving a yak
made more sense than the examples given in the op
- oh we should paint it
- we need a paintbrush
- I hear yak hair makes the best paintbrushes
- here I am, shaving a yak
made more sense than the examples given in the op
Coincidentally, this is also the first time I'm hearing about sable.