But if they're competent, they don't need the money, because they'll be able to work up to the point where they have as much as he did - according to the article, he started off as a "poor street hawker," so his belief that his children could do the same is certainly logical. They probably also have the advantage of his connections, better education, and so forth, meaning that they should be even more capable than he was. Also, if they're competent, lacking money might be good for their moral character, and encourage them to eventually do the same if they gather a lot of money, doing more good for society.
If they're not competent, it's better to give the money to the foundation he started, so that it can help as many people as possible, instead of being squandered. Sure, his children might need it more, but they wouldn't be able to do as much with it which would be useful to society, which is what he is trying to do.
Yeah, I'm not arguing against those points, per se. The dilemmic fallacy is simply a way to show the dilemma is subject to perspective, and therefore not as steely as it may seem.
Incompetence isn't an irreversible trait. A lot of people face barriers that make reversing the condition extremely difficult or impossible, but these typically aren't the children of rich people. Their problem is more likely one of never experiencing true need, and thus not understanding the risk of being incompetent.
I'm playing with his dilemma more than anything else, but you could also attack his assertion that the competent don't need his wealth. His children could be competent and unlucky, for instance, which could mean they need a lot of money: chronic illnesses, for example.
If they're competent, leaving them a lot of money won't do them any harm. If they're not, they need his money.
[edit] here's the classical example of this change in perspective: http://divisbyzero.com/2008/11/30/euathlus-and-protagoras/