Last June (almost a yr. ago) I wrote this blog
Cruisemates Blog Cellular @ Sea Can Be A Rip Off @ Sea – Kuki
While it doesn't relate directly to Verizon, it does relate to any and all cell phone providers, and it works the same way for each.
If your cell phone was on it would pick up service (from the provider) through cellular @ sea and thus result in costly roaming services. Even if you never used the phone. If it's left on, it "roams".