I'm opposed to the use of rBGH. Stating falsehoods doesn't help the cause.
The absence of evidence that rBGH ends up in milk isn't for lack of trying to find it.
I get organic milk because it tastes better. I suspect that means it's more nutritious, and further suspect that's because of the growth hormone, not the absence of some pesticides (but not others!) in the feed.
To preemptively correct a misconception which many people have: nutrition labels are based on what the government legally allows producers to claim, it isn't the result of some test performed on the food inside the package.
Just like a huge tomato doesn't have much more lycopene than a smaller one with the same genetics, it makes sense to me that most of the increased lactation from rBGH is just water.
Might be bad for the cows too, I mean I doubt it's good for them. But I consider it cheating and think we'd be better off without it.