Stopped with the brake on, the torque converter encounters some resistance to its internal fluid motion. If you were on a slope such that if you took your foot off the brake and the car stayed still, it has the same resistance, only now supplied by gravity rather than braking. The force that’s preventing forward motion (braking or gravity) doesn’t matter to the torque converter, so obvioulsy in this precise situation it’s a wash.
But on a slope where the car would roll backwards, you’ve got to rev the engine. This is equivalent to revving it in gear with the brake firmly applied. The more you rev, the more the fluid is heat-stressed. Consider that the transmission fluid is cooled in a radiator that’s at about 200’ F. That fluid gets HOT, and it does deteriorate. When the fluid breaks down, other transmission components can suffer to some degree. Avoiding overheating the fluid is a sensible thing to do.
Where the line is drawn between essentially harmless resistance (e.g., stopped at idle) and significant stress on the fluid, or how long it has to be revved to what engine speed to cause what degree of harm, I don’t know, and maybe no one knows. But every car manufacturer instructs NOT to hold the car on a hill by revving, transmission overhauls are expensive, and there’s no sound reason not to use the brake instead.