ApMax is absolutely right, and numerous users have been affected since 10.6.2, and remain affected to this day. Various system updates (10.6.x) or upgrades (10.7+) solved NOTHING.
Since the beginning, well-meaning people like Balltwo came up with what they claimed were solutions, but to no avail. And since the beginning, various people duly filed bug reports with Apple, with the same result.
For anyone who's not aware (or hasn't read the other pertinent threads), this icon random rearrangement problem does not only affect the desktop, but other folders as well. This alone makes it obvious that alleged "solutions" (like the one from Balltwo) are no fix, as they only target the desktop (as if this were the extent of it). And for the record, creating new admin accounts or reinstalling everything from scratch after wiping the disk have all been tried already. No go.
Whoever said they suspected something is deeper than some Desktop malfunction, is spot on. This bug has something to do with the system's guts. Apple knows it (witness the various bug reports which have been submitted), and has neglected to address it for far too long. Sounds like quality control resources are only devoted to iOS these days.
At this point, I'd bet beer that we'll still be affected under 10.8.