Okay, Saul, so if you were working a minimum wage job (@$14,000/year) and your ex was making $100,000/year, you would be too "proud" to accept child support so that you could afford decent housing for your children when they stayed with you, or to be in a safe neighborhood, or to feed them good, healthy food? I know that's not the situation you're in, but it is the situation that women sometimes get in after being out of the workforce to raise children and then having to support themselves and their children.
Your example conversation doesn't provide enough information to judge it. How much child support does her ex owe? What is the difference in their salaries and how much is that support needed to provide for her children? You situation (where your wife and your resources are comparable) and hers may be quite different.
My personal opinion is that all things being equal, if you cannot support your child financially, then the other parent gets custody.
Of course, all things are never equal. Certainly, financial support is not all that children need, and the financially more well off parent is not always the one who wants full custody or is willing/able to provide all care and all that entails. Money does not make one parent better than the other; it just means they have more resources.