At the separations and details typically provided by the treads it is difficult for the compressed flanges to deform freely in lateral torsional buckling as a free beam would do. If only linking the compressed flanges we might only be thinking in one somewhat risky relative bracing where the unused stiffness against LTB in the other stringer braces the one being considered against its own LTB. For just 2 stringers that's an uncomely proposition, except on overdimension.
In any case the fact is that threads and their support many times (but not always) engage the stringers in such a way (threads joined to the webs, compressed flanges restrained against torsion by their union to the thread and vertical plate of the step) that the outfit becomes reasonably stout against LTB of the compressed flange, say, the upper flange.
Only when unable to restrain torsion by the general weakness of the thread your conservative assumption will be the required one. There's a way out of this and is modeling the stair with all details, even providing initial imperfections, with P-Delta and P-delta, then (segment) member analysis by formulas in the code(s), and you will know if you are safe against this in whatever the case.