This is not always necessarily so in German. Though as a general rule, it is alright.
For instance: "Der Junge mag keine Erdbeeren" (the boy does not like strawberries).
But you can also say: "Der Junge mag Erdbeeren nicht".
or another example: "Sie lädt keine Fremden ein." (she doesn't invite strangers) you can also say: "Sie lädt Fremde nicht ein."
Because the verb isn't being negated. I don't know about Danish, but in French it's the difference between "Il ne porte pas des vetements" and "Il ne porte aucun des vetements". In the first instance, he is not wearing clothes. In the second, he is wearing "not-clothes" (as we say in English, "no clothes").
Just because someone is wearing clothes doesn't necessarily mean they are his. My daughter borrows my jacket all the time because it's comfy, but it's still my jacket even if she is wearing it.
The sentence here doesn't denote ownership. To say "The man is not wearing his clothes" you'd probably need to say "Manden har ikke hans tøj på." The "hans" here means "his".