SE stated that main are for HQ and offhand are for increase in materials synth'd
I don't remember them explicitly saying so. They just said your tool choice can affect your yield or HQ chances without specifying which does what (especially since it probably varies by craft and synth and it's also SE we're talking about).
Well I for one can't say if it's true or not but if what people are posting in the database is true there may actually be some truth to this.
Some examples are: Hempen Yarn
and Hempen Bowstring
As you can see the main hand tool, according to the links provided, yields +1s 2s and 3s. While the secondary yields more NQ items.