Ok, so I went into Verizon again today with some in ear monitors. I tested 3 phones by playing music and lowering the volume all the way and also by changing the ringer volume. Note: Clicks when music started playing/paused and when changing ringer volume were audible on all 3 phones.
First up was my own OG Droid. I noticed no high pitched sound, only a slight hiss which as I recall has always been present. No big deal whatsoever. Second I tested the Bionic. Needless to say, it failed miserably. I still can't believe this slipped by QC. Third, I went for the RAZR. Good news! No high pitched noise! All I was able to hear was a slight hiss and a tiny bit of crackling almost like a needle on a record with no music.
So, I can confirm that in the test unit at my local Verizon, the RAZR has NO headphone whine. All that was audible was a normal hiss that can be heard on every smartphone I've owned/tested. I'd say if the Bionic was a 10 in audible noise the RAZR would have to be a 2 or 3. Remember, I tested this with in ear headphones, so if you're going to be using over the ear headphones or some buds, the noise will probably be even less audible.