Let's take the example of the photo of Angela Merkel and the Syrian refugee, mentioned in the article. If you publicly declare, that the person on the photo is a terrorist, and the person is not, you are clearly breaking the law, because you are damaging the persons reputation with arbitrary false claims. If you mention something as a fact, which you cannot prove, you are held responsible for the consequences of the claim and you are prevented from repeating the false fact.
If you would declare "There have been rumours, that the person on the photo is a terrorist", the legal perspective is completely different. Because there obviously have been the rumours this is not a false claim. It now depends very much on the context. If it was known to you, that the person is not a terrorist and you declared the fact of the rumours, but in a way, that it nevertheless makes the person appear as a terrorist, you might be breaking law, but this now depends very much on circumstances and can only be deciced individually in a court case.
Saying "I completely believe the person is a terrorist, even though there is no prove" would most likely be covered by freedom of speech in Germany, because the claim is not presented as a fact, but an opinion. There are limits here (you cannot hide abuse and revilement in an opinion), but interpretation is extremely generous in those cases and makes, in my eyes, the biggest difference to systems like China.
I am completely fine with this approach. I think that a proper differentiation between fact and opinion is the key for a healthy social discourse.
How would anyone be able to defend himself against false claims, if any utterance of whatever was covered by free speech?