The same way judges can throw out a case without going to trial. Checking if the complaint makes sense, if it represents an actual violation as described, etc. Anyone dealing with the public knows that a huge chunk of the complaints don't even pass that bar.
Remember that the Data Protection Directive, which already allows citizens to ask companies if they have data on them and to correct incorrect data, has been around from 1995, yet there hasn't been any mobs ruining companies.