Issue repainting existing cabinets on flip. Is contractor right?

[Katie Neason]

I am on my 4 SFR flip. So I have just enough experience to think I know more than I do. We are repainting the existing kitchen cabinets. According to the painter he has put 4 coats of primer and 2 coasts of paint (whitish color) and the wood grain color is bleeding through. He says the issue is that it is a wood grain skin/veneer. He wants me to pick a darker color. I would prefer not to and am skeptical. He is using Home Depot's Glidden Pro Paint. Before I do I want to get options from others who have experienced it. Here are some pic before and after. Thanks!