I'm wondering if being Truthless could be a Shin cultural issue more than a spren/Herald/Oath breaking type thing.
In the Rysn chapter, Vstim mentions that he acquired Szeth by way of Thresh/the farmer. Vstim tells Rysn that the farmer's warriors are "the lowliest men like slaves" and they are "traded between houses by way of little stones that signify ownership". He says, "any man who picks up a weapon must join them and be treated the same." In another chapter, it was mentioned that the Shin gave Szeth the Shardblade and sent him out into the world.
Maybe Szeth was the farmer's slave and aspired to a higher social status, or maybe he picked up a weapon under some circumstance and refused to be treated like the other warriors? This could also fit if he was high born and picked up a weapon, but refused to be treated like a slave. In refusing a weapon, he was punished with carrying the Shardblade.
I don't know. I even looked up the word truthless to see if that would yield any clues. I found the following meanings: devoid of truth, dishonest; spurious (of illegitimate birth - maybe there's something here?); corresponding to something without having its genuine qualities; falsified or erroneously attributed; deceitful nature or quality.
I'm probably way off, but maybe being Truthless means something along these lines.