A seven-level wipe is overkill, by about five or six levels. Once magnetic data has been overwritten, even once, it is gone forever.
An ancient paper by Peter Gutmann mentioned a theoretical possibility of recovering badly-overwritten data -- but this depended entirely on sloppy tolerances, low data densities and imperfect magnetic properties prevalent at the time. Data storage density has increased by several orders of magnitude since then. Heads don't wander to the sides of tracks anymore, and a "one" that used to be a "zero" no longer looks any different from a "one" that always has been a "one". Even if you do manage somehow to identify correctly a few thousand bits, out of the hundreds of billions on the disk, you won't have a clue what they represent, nor what belonged in the gaps between them.
Once data has been overwritten, even once, it is physically impossible to determine what was there before. Certainly not using software -- that's the whole point of how a hard disk drive works, for crying out loud -- and not even using hardware. Digital media are driven right into saturation, right onto the bit of the (already very narrow in the oxide grades preferred for HDDs) Hysteresis Loop where the two paths merge -- the bit where there is no way to determine which way you took to get there. (If you are really paranoid, then two overwrites in a row -- one with all ones and another with all zeros -- will set every bit on the drive to be a "1" that used to be a "0". If a drive full of ones looks suspicious, then use a pseudo-random bit sequence: use the same seed for both passes, but invert everything on the second pass. Now every bit on the drive will be either a "1" that used to be a "0", or a "0" that used to be a "1".)
Think about it: Magnetic storage has been used, in one form or another, throughout almost the whole of the history of computing, all while the prices of various components have risen, fallen and crossed over. If it was ever possible to recover past data, there would have been a stage when it was economically viable to exploit the technique to increase storage density. In fact, no computer has ever been built which uses this effect. The closest any machine has ever come was a reel-to-reel tape recorder from the 1960s which had a "trick record" button which, when pressed, disconnected the erase head; allowing you to superimpose two recordings. For instance, you could record yourself playing an instrument, then rewind and add a recording of yourself singing. Except it was crap; because, even if the double recording didn't sound as though it had been made in a long tunnel stuffed with cotton wool, the lack of monitoring meant it was impossible to line up voice and music accurately. This is why you don't see "trick record" buttons on modern tape recorders.
No data recovery firm can recover overwritten data. Not even agencies of the US government are above the laws of physics. On the other hand, you do usually have to try very hard to overwrite data. Windows in particular uses virgin disk space in preference to deleted files, precisely so that deleted files can be recovered for as long as possible (earlier DOS versions overwrote deleted files in preference to using virgin space, precisely so that deleted files would become *un*recoverable as soon as possible -- this behaviour was changed when customers complained); and when you save a new, longer version of a file with the same name as before, chances are the new version will be saved elsewhere on the disk just to keep the file in contiguous sectors for speedy access. The old version will be left intact, but marked as "free for use". (If you fill your disk with a load of junk files, so there is no more room to save anything, *then* delete some files, now the only place anything else can possibly go is where those deleted files used to have been.)
The official advice calling for physical destruction of used HDDs is mainly psychological: it convinces enemies that the USA has methods for recovering data, and it convinces citizens of the USA that the US government's best overwritten-file recovery methods actually involve doing something to the HDD rather than its owner. Drive manufacturers aren't falling over themselves to correct this misrepresentation, either; since if people are unnecessarily destroying serviceable drives, it means they sell more new ones.