Welcome, maxie. I think you’ll struggle to prove such a narrow definition, since the root comes from long before anyone had taken horses to America let alone hired them out.

The word comes from Old French estable and ultimately from Latin stabulum, derived from a Latin root (sta~ from stare) that meant to stand. For ages it was used to describe a stall for all kinds of domesticated livestock, not specifically horses: compare for example the modern French word étable, which means ‘cowhouse’.

The OED also gives this other meaning suggestive of other kinds of whorses!
2. b. slang. A group of prostitutes working for the same person or organization.

There are a family of related words, including establishment and stable (in the ‘standing firm’ sense).