That is incorrect, at least for magnetic media. Companies like this recover overwritten data from magnetic disks all day every day.
When every sector has been overwritten, the data is gone for ever. A formatted drive or one where files have been deleted can be recovered but one where every sector has been written to, the previous data is gone forever.
Contact your company you listed and tell them that you accidentally wrote new data to every single sector on your hard drive. Ask them if they can retrieve your old files. They can not.