It's the same thing for the terrorist attacks. As soon as there's an attack, the terrorists claim it, whether it's linked to their movement or not. I think I've answered your question, but I will answer it more positively.
Yes, they can claim responsibility for an attack or make it appear that they are behind this or that attack, precisely to create fear. They want to send the message that if we do something, they can do something in response that will have a very significant impact. This attack is an example, even though it wasn't the Russians behind it. As you just said, this creates a climate of fear. It's said that you can have a significant impact through a reaction or a cyber‑attack.