Many dogs come in many colors and there seems to be a rising confusion wheras some believe that just because a dog is a particular color, it goes back to the Pêtre dogs of the 1970, which is not necessarily true, but just a selling gimmick.
This Poodle site explains the situation of the Poodle very well. I also happen to agree that the PartiPoodle/Arlequin was and is a real poodle and not a bicolor dog as it is qualified by the French Poodle club.
If you look carefully at the Poodle colors on the page you will see some very Modern Barbet colors, and also coat textures. ( Or is it the Portuguese Water Dog?)I wonder.
I would add that Poodle x Portuguese Water Dog both coming in white and black, could also explain it. As Far as many Barbets are concerned, it is the Spanish Water Dog who did wonders.
The Poodle’s very fine coat type extremely curly is not at all the Barbet coat type and nor are gray or tricolor stripes on the legs. Nowhere does it say in Barbet standard that black and gray, or black with tan, brown and sand legs is standard accepted colors.
Last, but not least, there is also a question of morphology in the breed and with that come measurements. Consider the head type and the ear set.