Did they really suggest white noise? I imagine it was pink or brown noise? As I understand it, white noise is the only damaging one since there's no "falloff" to the PWM, it's just "white" or "black," so the spikiness of the modulation can be damaging.
The point of the white noise in TRT is not masking the tinnitus so it is not played loud.
The white noise must be played below the level of the tinnitus, so one can hear both sounds simultaneously. Doing so, in theory, the brain learns to reclassify the tinnitus as an unimportant signal (noise).