That was true for the old hard drives, you know, 5.25" Full Height, 20MB... Current 1-2TB drives pack the data so densely that is may well be impossible to recover even one "layer" of data.
In any case, no software would be able to recover overwritten sectors simply because even if the hard drive does not flip all of the particles, if flips enough of them so that it can read back the data.
(did you try running your program after zero-filling the drive?)
FBI, CIA and others can have equipment sensitive enough to recover overwritten data from the drive. But if you are worried about them, you should already have the drive encrypted and use multiple passwords (so that when they use rubber hose method for decrypting, you tell them one password that decrypts less important information, that is, if they manage to pull out the encrypted file after you zero the drive).
In fact, once I received refurbished hard drives full of financial records of business.
They probably didn't even try to erase the data.