A red horse with a flaxen mane IS visually different than a red horse with matching mane and tail. I would venture to say that it is adding more specificity to call them different things. If my mom told me she saw a chestnut horse running loose near the house, I would know I wasn't looking for a red horse with flaxen mane and tail. It wouldn't be very helpful for me to have to keep in mind that she could have meant a red horse with a flaxen mane and tail OR a solid red horse.
I would also venture to say that they ARE genetically different. Perhaps the base color is the same, but something is going on in the genes to give some red horses lighter manes/tails while others are solid red.
Thus I assert that people are not "perpetuating a falsehood", they are stating the obvious as they perceive it in the immediate and tangible world.