Yes unfortunately, one of the many pitfalls of british car insurance.
As for the wheels, i cant really see them punishing your cousin for getting them refurbished so that should be ok since it doesnt add performance and they are the originals.

Even if he goes through the courts to claim from the uninsured driver it's likely that the guy doesn't have the money to pay up if he couldn't afford the insurance in the first place. So he either will have to pay what he has (maybe 20p and a packet of polos?) or pay back at about £1 a month for life - which is useless really.

Some insurers don't take away your no claims if hit by uninsured drivers, but most see it as a way of not having to give you a discount anymore (good for them eh? no need to care for the customer when they can fill their wallets!) so I'd check. Depending on damage it's sometimes cheaper NOT to claim in those circumstances. Even if you don't lose you NCB the fact of having a claim will still raise the premium for the next 5 years so tell him to think long and hard about it.....