This business is a top-of-mind luxury brand in their market. They literally have NO organic backlinks. In fact, in their market the competing businesses just don't know about backlinks.
Their search traffic includes about 45% brand name searches. There are no social mentions for them or their competition. Again, it just isn't part of this market. What they do have is a website whose user stats are outrageous. Bounce rate is under 25%, with 14 minutes average time on site.
Admittedly, that's not 100% proof but it's highly suggestive. 100% proof is very hard to come by in today's Google. As I see it, Google just knows that this business is what users who make these queries are looking for most of all.