It's my understanding that it was believed that a slave's presumed loyalty to his master would compel him to lie on his master's behalf, and only torture would ensure that the slave might give truthful testimony. Considering that not all slaves were quite that loyal to (or even overly fond of) their masters, I fail to see the logic, too, in torturing them.
Pliny the Younger wrote in one of his letters ("To Macrinus" LXXV) of "a certain lady" who suspected that her son had been poisoned by his freedmen. Pliny was counsel for the defendants, and he tells of how his clients were acquitted only after the torture of the servants.
In later years the Emperor Hadrian, as a humane act, issued a decree limiting the routine use of torture of slaves, so that it would only be used as a last resort.
-- Nephele
Thank you so much for responding, Nephele. The situation comes up rather often in the series, but never in a context where the slave owner's interests are at stake -- just things that a slave would have noticed and testified to about other people -- consequently, I couldn't make sense of it, but your explanation puts it in context for me.
So this was a law that was applied to all testimony of slaves, regardless of whether or not the logic of the law applied to the circumstance... Bureaucracy at work!