this is not true. It's likely the invisible to animals or no warrant option or some single option, not 'any of them', and likely is situationally does this, like if you are in a town or something, etc.
i tested it with every option, youre right, Easier Hunting causing it, 🙁
Just try using Super Cowboy. It makes all the "bars" stay max (not the cores tho), even horse.