Totally annoying, isn't it? With that big soundboard picking it up and amplifying it, it drives me nuts.

I would bet it was more likely Protek lubricant on that swab. Others use graphite-based lube like mollybednum. Protek (a Teflon-based lubricant) is better as it's hydrophobic and won't absorb moisture, but it's expensive and hard to find. So I crawl under the piano and use two fingers to grasp the wooden rod on top of the lever that connects the sustain pedal to the action mechanism and lift it up (doesn't take that much effort--those dampers and the mechanism are light). Then, I use a swab with mollybednum to lube the underside of that wooden rod and *also* the leather pad on top of that lever the rod rests on when the two are contacting. Gets rid of that squeak.
If yours is an upright, it's the same general deal, but you'll have to pull the front lower panel to get at it.