The graphics / badges etc is just silly, a badge would be a modification? So a de-badge would be a modification as well. None of their business I would say as it is not a risk factor.
All those 3 series rep drivers with M badges would have invalid insurance than
As far as I know, if you don't declare something, you get back "standard" spec. Wheels are a little different as they are more likely to be stolen and you can't expect them to cover those without knowing about it.
When I declared my mods, they wanted to charge extra for my Factory specced Bluetooth as it made the car more likely to be stolen according to them. That is when I lost my rag and asked to speak to a manager as it became a complete nonsense.
If an insurance company was going to try to weasle their way out of paying beacuse of say my Intravee iPod interface which I did not declare, I would take them to court.