Well s939 platform is pretty old, i got off that platform just when 1GB PC3200 modules started showing up and nearly all would of been double sided back then, so haven't looked at that platform in several years and i guess it's same for most forums. Back then that was the info that was going around
Only thing is to clarify what AMD meant by quad rank - if them meant 4x slots populated or not. Reason is as i understand it, single sided modules are usually single rank, and double sided are double rank. Don't see quad ranked DDR1 modules in consumer desktop boards. So they could mean quad rank as in 4x dimm slots populated with single sided modules.
But as you said you've been running this config (4x1GB PC3200) for a while now - but i misread your post as to you not being able to run it due to an issue you had which you didn't initially elaborate on (hdds).