Old-style hard disks and floppy drives were formatted by using the "ordinary" write process to write synchronization and sector identification marks in a manner that was blind to whatever had been on the disk. During normal operation, to write a sector, the drive will listen for the synchronization mark that's followed by an identifier for the proper sector. It will then turn on the write head and blindly write a sector's worth of data.
Some utilities, of which I would expect SpinRite to be one, will read each track of the disk, reformat it, and then rewrite the track with the data it had just read. This would probably not be needed unless one wanted to change the sector interleave after getting a faster computer, but hard drive sectors did sometimes fail; it's unclear to how often failure was caused by gradual degradation and to what extent it was primarily caused by areas of the disk whose coating wasn't quite as good as it should have been, or an inferior region of coating which allowed magnetic domains to spread unusually fast. I would expect that on some, perhaps many, hard drives in the 1980s there would have been areas that would work more reliably if periodically refreshed, but there would also have been many hard drives that would not need such treatment. Today a sensible attitude toward storage media would be to regard any media that can't reliably hold magnetic domains indefinitely as meriting immediate replacement with media that can, but technology was nowhere near as refined in the 1980s as it has become in the decades since. Even if one replaced a hard drive that wasn't fully trustworthy, there would be practical no way of knowing whether the replacement would be any better.