First, there is little doubt that statutory third-party insurance applies at the Ring. Whatever else it may be deemed to be, the Ring is legally a road, and insurers must cover their legal obligations.
However, this does not mean that you are comprehensively insured on the Ring. More and more insurers are using various mechanisms to exclude the Ring.
Some policies specifically exclude 'track use'. Since the Ring is legally a road but also undeniably a track, this policy wording could be interpreted as letting the insurance company off the hook. At the very least, it is likely to lead to extremely long and potentially expensive arguments. Some German policies go even further and specifically exclude the Ring by name: in those cases, there is no doubt at all that you are uninsured.
A number of companies now exclude 'de-restricted toll roads'. Although they don't name the Nurburgring, it's hard to think what else this could mean. I used to name these insurers, but there are now so many of them - with more being added all the time - that I've given up trying to keep track of them all.
Other insurance policies state that they cover 'normal road driving', which gives a mechanism to argue that the Ring - even though a road - doesn't constitute normal driving.
It's thus important to read your policy document word-for-word.
Even if your policy appears to be ok, I think these days you have to be prepared for your insurer to use any excuse they can to avoid paying-out. I thus strongly recommend that you consider your vehicle uninsured on the Ring, and drive/ride accordingly.