When deriving the minima, the classical approach is to say
$$ \frac d 2 \sin(\theta) = \frac{\lambda}2$$
therefore, $$d \sin(\theta) = \lambda$$ It can then be shown for any integer value of $\lambda$. But why couldn't you say that the 2 point sources that interfere destructively are the full width of the slit apart, so $d\sin(\theta) = \lambda/2$, therefore $d\sin(\theta) = \lambda/2$ for destructive interference, which wouldn't be an integer. Maybe I've misunderstood something.