Now of course, this may be a natural reaction to some predator native to their natural environment, right?
Since North American llamas were imported from South America, I looked up what relatives of dogs live in South America. Now, there’s lots of canids in South America, but they are considered a relatively recent addition to South America’s ecosystem, and come in a variety of colors. This of course means, that such a fear is less likely to be ingrained at an instinctual level, and that all dogs, regardless of color, should be feared equally.
However, scientist believe llamas themselves originate in Central America. But the story here is similar, less species of dogs, but a variety of colors.
But, perhaps it is not dog specific, but simply the quadruped body shape combined with black skin/fur they fear. Both panthers and spectacled bears live in these areas. Could it be one of these predatory creatures they fear, or something even more sinister, like the chupacabra?