Actually it is misleading by them( and you ) to assume that in C, an unsigned int can represent values larger than the largest signed int value.
In other words, C allows that UINT_MAX == INT_MAX, in which case you will overflow.
If they made that assumption, they should explicitly mention it, but they didn't.
> Update 17 Feb 2008:... ...Now that we've made this change, we know that the program is correct;)
It seems the article is aware of the irony. Another update would be in order.