The claim that 'dogs can only see in black and white' is false.
According to an article by Scientific American, the idea that "dogs could only weakly see color, if at all,"1 which was claimed by author and optometrist Gordon Walls in his book The Vertebrate Eye and Its Adaptive Radiation. This belief took off in the 1940s and was later debunked in 1989 by ophthalmologist Jay Neitz and his colleagues who "discovered that canines could see blues and yellows but not reds and greens."1
A separate article by Ragen T.S. McGowan, a pet expert and research scientist from Purina, states that "A dog’s retina contains a small amount of cones (cones are photoreceptor cells in the eye’s retina that allow us to see color). Humans have three types of cones in their eyes while dogs only have two. This means their vision is limited to certain colors."2 Also according to the article, McGowan states a canine's vision is near sighted, and it's believed that most dogs have 20/75 vision, in which that means "they have to be 20 feet away from an object to see it, compared to humans who can see it from 75 feet away."2
This claim is outdated and strictly just a myth that has been debunked time and time again, and can also be exaggerating and misleading to readers. It's also unclear what their intent was by sharing this claim and giving no evidence or further description to follow up their claim.
www.scientificamerican.com/article/what-colors-do-dogs-see/
https://www.purina.com/articles/dog/behavior/understanding-dogs/can-dogs-see-color