Sorry, I don't understand your explanation. Could you expand upon it?
It seems to me that the negation does come before the verb it's modifying in both sentences from the original post.
I thought the reason for this word order was the V2 rule.
I will be brave and agree with you here, although I'm not a native speaker. It is the v2 rule in action with a dependent clause which causes the swap of the two words that the Original Poster asked about; namely "kan de" insead of "de kan."