You are using custom template, and register form is template build in action. If you open product with default clean template, you will not see this. To hide/remove you may contact with theme developer or simply hide it by jQuery or css.
They have confirmed there isn't anything they can do. As I stated before, I tried this on a clean theme and it it's there too, so I'm not sure what to do.
Thanks for the help,
Are you using any third party plugins? Have you try to disable it one by one? If this is shown also at the default theme, means this is done by plugin/widget. Not sure which one, as I do not know which you are using.