No, there aren't any "arguments". There are different rules for different situations.
Go back and read the third and fourth paragraph carefully. The article points out that the rules are different for a "child" (son/daughter) than for other relatives (such as a grandchild), and the examples are about a non-child (grandson).
For a "child" (son/daughter), scholarships do NOT count as them paying for their own support. For a non-child (such as a grandchild), they do count.
