The article mentions that on Mars, with 0.38x Earth gravity, there will still be challenges, so I expect you need a significant fraction of 1g for the problems to go away.

It's not an absurd question. The threshold value is the one that breaks surface tension and effectively pulls waste away from the body. It will be more than a few hundredths g but less than 1g.

Unfortunately we have basically no data on the effects of partial gravity, in this context or any other. We can try flying partial-gravity parabolas in aircraft and simulate a Martian toilet the same way they tested the design for Skylab; I don't think this experiment has been done.