Looking at the carfax I would say the mileage is legit. Possibly used as a taxi or a limo. Atlanta has a taxi rule that they can not be over 5 years old. So 5 years as a taxi and traded in .
While the black book shows the value in the mid 30s, It'd take a very special buyer to fork over $35k cash for ANY vehicle with 350k miles... I think that once you get outside of fairly standard parameters, the book values become less accurate because the pricing algorithm isn't really built for these cases. The mileage deduction is linear, but market reaction to way out of normal mileage isn't linear....
I've been looking at 200 values for many years, and my back of the envelope calculations have usually showed that after the first 3 years in a 200s life (where the only significant depreciation occurs) the depreciation hit for miles is small - usually around $0.02-$0.03/mile for an older 200 and $0.03-$0.05/mile for a newer 200. It's incredibly low depreciation for any vehicle, especially an expensive luxury SUV. The blue book values are showing a similar depreciation curve based on mileage, but it does not take into account the (actual or even perceived) useful life of the vehicle.
The vast majority of consumer vehicles are fully depreciated after ~200k miles or sooner and are either cost prohibitive and/or unsafe to keep on the road beyond that. Most Land Cruisers have what I would consider an indefinite lifespan however, and they will keep running as long they're maintained and fed gasoline (keeping them away from rust is important too). That said, the average consumer is terrified of anything with miles in the 6 digit range, so the pool of buyers for anything with 356k miles is insanely small. Those few buyers are value shoppers, and if they have $35k sitting around, they're going to spend a couple grand more for a 200 with 80% fewer miles. Considering all the excellent new cars that have come out in the last couple of years in the $30-50k range, the average consumer would far rather have something like a brand new Kia Telluride than an "ancient" 200 with 356k on the clock for the same money. In fact, I most definitely would take the Kia over a 356k mile 200 without a second thought.
The only way this thing sells is they find one of the 3 or fewer people in the country who would consider it with the miles at the asking price, or they will drop the price to a reasonable level. I sold my clean 08 LX with 172k miles for $22.7k, and I think that was a good deal for the buyer. This 2014 has a couple nice features not available until 2013, but it's 99.99% the same vehicle as the earlier trucks. If I had to put a WAG estimate on the right selling number, I'd say somewhere in the low $20k range would do it. If it sells anywhere in the $30k range, all of our trucks just became much more valuable IMO.