BaT operates at the intersection of on-line auto auction and social media, both of which are full of potential for foul play. How could you ever know whether the commenter was acting in good faith or a friend of the seller, or actually the seller? I think some of the high prices are prima facie evidence that a trusting naive buyer has been duped. BaT itself is probably legit but I would not be surprised if there was a BaT expose someday. Too many of the prices smell fishy.
There is also a premium for selling on BAT, one might say it attracts connoisseurs of the auto world and one's that are willing to pay extra for a great example.
even though we'd be able to find a similar lx likely in better condition for cheaper with that low mileage in cali you'd be looking at 10-13k, it can also take up to a year as you'd have to be patient waiting for a prime example and hope someone doesn't snatch it from you... someone with spare cash may not want to do that and just accept the premium.