Car appreciation... the aesthetics, the engineering, etc

You have no liability except for yourself. So in the unlikely event you spin off and total an Enzo, you don't owe the driver of the Enzo any money. He would be stupid to turn up without trackday cover. However you yourself are not covered by your insurance so if your car was written off, nobody will bail you out unless you had previously taken out trackday cover. I have known some to er... tow/drag their cars 20 miles down the road and then call the AA, but the insurance companies are getting more clued up to that. A track-y car within 50 miles of a track will be investigated, CCTV, phone the track etc. Marginally more successful but even more fraud-y would be to trailer it home, park it outside the house, and say someone smashed into it during the night then drove off.

I'm not sure he'd see it that way. I have heard stories of people having incidents with other cars participating and it being less clean cut than "oh don't worry,we're both on a track so you look after yourself and I'll look after myself.."
That said, in all the time I've participated in trackdays (getting on for 15 years as a passenger and a driver) I've never seen any problems like that.
Just be vigilant, drive within your limits and you'll be fine.