Ending points of the root locus
The problem with your example is that $\infty\cdot 0$ isn't necessarily equal to zero. The only way to judge what is happening in the limit $K\to\infty$  is to divide the original equation by $K$:
$$\frac{D(s)}{K}+N(s)=0\tag{1}$$
Now it is obvious that for $K\to\infty$ the actual value of $D(s)$ is irrelevant, as long as it is finite. Consequently, the only necessary condition for $(1)$ to be true as $K$ becomes large is that $N(s)=0$.
This problem is a bit similar to the problem of determining the limit
$$\lim_{x\to\infty}\frac{x}{x+c}\tag{2}$$
The value of the limit $(2)$ is independent of the choice of the constant $c$, which becomes negligible compared to $x$. The same is true in the first equation of the question: the actual value of $D(s)$ becomes irrelevant compared to $KN(s)$.