Trackday insurance pretty much never covers third-party liability, it's cover for your vehicle only. My understanding as a non-lawyer of track day (and race) liability is that it's quite different from road liability. In a road accident, liability usually decided against one party or the other, but can be proportioned (for example, I was speeding but you pulled out in front of me without looking, so it was 75% your fault). For trackdays, like many sports, you are assumed to be taking on a risk by taking part. If someone has an incident which might reasonably be expected on a trackday (like losing traction and spinning off) and they take you out, it's not their fault, it's yours for taking part. On the other hand, if they do something stupid like ignoring overtaking rules or continuing to drive fast after a red flag is thrown and they take you out, you have every right to claim from them. The same way as a legal tackle in rugby that caused injury would be OK, but punching another player or tackling a player who doesn't have the ball would not.