No. You're either mis-remembering, or got your info from someone ignorant of the issues involved. There are various reasons why you don't want to completely fill up a file system, but that is only tangentially related to hard drives. Certain operations on certain file systems start getting very slow (or fail completely) when there isn't much (or any) free space left. It's even possible under certain circumstances to end up with a filesystem so full that one of the operations that fails is 'delete'. That's an exciting one.
That said, I've used quite a few different file systems (FAT12, FAT16, FAT32, NTFS, HPFS, HFS, HFS+, ext2, ext3, xfs, etc), and done horrible things to many of them, without any problems. The short answer is: don't worry about it. The longer answer is: try to leave 5-20% of the file system free, depending on what you want to do with it. 5% should be fine for most things. Defraggers usually want closer to 20%. If you end up filling the drive, things might start to get slow, but nothing should break. And certainly the drive doesn't care one way or the other - its reliability is independent of how full it is.