Not quite - modern magnetic drives still have tracks wider than the read-write head so that atomic-level alignment isn't necessary. There may be far less "overwrite" than there once was, but if a newly recorded track is not *perfectly* aligned with the last recording then there may well be several percent of the previously recorded track that remains unaltered (consider the worst case scenario case that the previous recording in this track was written at the smallest radius allowed by actuator tolerances, while this pass is at the maximum radius allowed). Now, recovering that data will probably require removing the platters and analyzing them with much higher resolution read heads, but it can be done.
I was more addressing the problems with flash though - in order to disguise degradation modern flash drives typically include more capacity than is addressable by the host system. Fill it to the brim so there are zero bytes free, and there's still several percent of the total drive capacity that is sitting unused in the reserve pool. The only way to overwrite that (barring a OS-accessible "secure wipe" command implemented on the drive) is to generate sufficient churn that the internal wear leveling algorithms cycle through every byte of the reserve capacity at least once. And since you probably don't know the exact algorithm used or wear levels of the drive to begin with, more is better - after all you have to tease out the most heavily used page currently sitting in the reserve.