Claiming responsibility for an attack, whether the claim is true or not, puts a group in the advantageous position (if they are astute enough to make use of it) of being able to multiply their effectiveness while exerting less effort, by issuing threats and warnings about potential attacks, whether these attacks take place or not.
If a group has established its credibility as a dangerous player, any threat they issue must be taken seriously; the response to the threat will itself cause significant disruption, even without the group actually undertaking any action.