Unless Doe can provide any actual reason for believing they have his data, and as long as the data handling process of the company is sound, the regulator will just close the issue. At least that's my experience.
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.
What reason could anyone provide? (even that a company like fb still has your data) Or that a company sold it illegally? Or that random targeted ads you are seeing are the result of data from any particular company?
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.