It was a private reserve owned and operated by a Louisiana oil exec. It is assumed that both were comped for the trip. The details are still murky. Scalia got a free ride on AF 2 and a free hunting trip at a retreat owned by an oil exec though. That much is not in dispute.
It wasn't a very bright idea.
A couple of observations: most of the "news" I've been able to find via google.com isn't really "news" but editorializing and/or punditry. Not much hard 'n fast facts; maybe that is why you say the facts are "murky". Maybe the oil exec owned the land, but that doesn't mean he paid for the trip, does it?
This appears to be not unlike house parties hosted by any number of Washington "players", except that it is in fly-over country. No one on editorial boards really seem too upset when other SCOTUS members hang with the rich and famous in D.C....and lo and behold, no one follows through on all of those social events, who is there, and what possible "conflicts of interest" there might be.