Lou, It is quiet where we live so drowning out back ground noise doesn't apply. BB also has, but doesn't use sound discs of waves, water flowing, and forest sounds. I too, like "white noise". I have teinus?(ringing of the ears) and stark quiet makes me hear EVERYTHING! The dog shifting on the floor, the wind on the siding, a slight difference in breathing pattern, EVERYTHING! Heck I think I could hear the grass grow given half a chance! There is a CD in TARGET that is wonderful, possibly as a peace offering, its called SLEEP and has D waves, (ok who's got an oscilliscope or whatever) its very pleasant, perfect back rubbing noise!
Maybe that might give you some insite to why the radio/tv is on. When we were traveling to D's wedding, the TV was off, H's closeness was like a wolf standing guard and 'allowed' me, my guard, to drop and I could sleep soundly even tho in a motel environment. To compound that illogical presentation, H can't be woken with a bomb. He's the most sound sleeper in the world. I know this; ergo the above letting dn of the guard makes no sense.
Maybe to stress the I'll watch over you trust thing, with no expectations of ambush is what she is looking for. Possibly disarm her by playing some whitenoise, and a short backrub, cuz I think you get benefit from them too as a giving of yourself, and leaving to your own room. With LUCK, she may come visit you. It may work...*hugs*
Pity me that the heart is slow to learn
What the swift mind beholds at every turn.
Edna St. Vincent Millay