I sent verizon an email about this issue.
They sent me an email back, telling me how to turn the notification off, which would have worked if I owned a non-Verizon branded S3. I sent them back an email informing them of that, and got a call from Verizon less than 5 minutes ago.
I was told that this was a mistake by the manufacturer, and that they're working with Samsung to fix it.
I was also told the same thing happened with the Incredible 4g (which isn't a big secret that the Dinc4g is having this same issue).
I find it hard to believe that 2 manufacturers screwed up in the exact same way, but the lady did tell me they're trying to "get it fixed" as soon as possible.