This claim is false after doing through research I found on AKC it states "That idea that dogs can’t see color was widely accepted for decades, but new research and conclusions about canine anatomy and behavior have shown that while dogs can’t see the same colors humans do, dogs can still see some colors." 
My second source dogs naturally magazine also supports that this claim is false. Dogs naturally magazine says "Your dog’s eyes, on the other hand, only have two cones – blue and yellow. This is called dichromatic vision, and it means that while your dog can still see color, his perception of it is muted compared to a human. The biggest difference is that dogs can’t process red light, which can make it hard for them to distinguish certain colors."
From a simple google search it would prove that dogs have dichromatic vision and don't just see in black and white while the color they do see is quite muted it is not black and white as people have been lead to believe with the progression of technology researchers were able to figure this out.
https://www.akc.org/expert-advice/health/can-dogs-see-color/
https://www.dogsnaturallymagazine.com/what-colors-do-dogs-see/