How could the Stoics claim a person is just as happy on the torture rack?

By redefining "good". Most people count health, wealth and reputation among the good things in life, and think that being tortured, poor and friendless makes happiness impossible. The Stoics disagreed. They are especially known for teaching that "virtue is the only good", and that external things such as health, wealth and pleasure are not good or bad in themselves, but have value as material for virtue to act upon. Their reasoning was that only what benefits is good, and life, health, wealth and reputation, like their opposites, death, disease, poverty and low repute, neither benefit nor harm.

So the Stoics maintained that even on the rack, with a mutilated body, in pain and cut off from family and friends, the virtuous person is maximally happy. Their rivals, the Academic and Peripatetic philosophers, found this unbelievable: they argued that virtue is necessary for happiness but not sufficient. Aristotle, we are told, considered that conclusion too big a bullet to bite, and the Stoics fully embraced it.

That does not make the Stoic careless about health. Mainstream Stoics held that some indifferents, such as health, wealth and reputation, are of a promoted or "preferred" type, and the virtuous person will typically pursue health and take steps to obtain it, such as eating salad and exercising. Being healthy rather than unhealthy simply makes no difference to her happiness.

Ancient critics called this incoherent: how can something be indifferent to our happiness and yet rational to pursue? Scholars still argue about whether the Stoics have a good reply.