Testing would be the only I would believe this horse is palomino. And it's the only reason I believe the other horse is. I'm going to say it's rare for one to turn dark like that. And w/ the OP's horse coming from an unknown background we don't even know if it's possible. Yes someone said he was, but based on what the OP has said about them it doesn't really seem like they know what they are talking about. The fact they called him a 'purebred' palomino was the first sign to me, that could easily mean he was out of two palominos (which someone might assume would make a horse 'purebred' palomino, in which case I once owned one and she was sorrel!), which would also make it possible for him to be a chestnut (25% chance).
If I had bought this horse w/ the history they have I would call him liver chestnut. If I was just crazy currious I 'might' would have him color tested, but only if there was something that made me think he was different then he appears (the only thing I can think that would do that is his ped not backing up his color (for example if one of his parents was cremello), or photos or someone knowing he appeared palomino as a youngster), and some random girl telling me he's palomino wouldn't be it, I've heard plenty of silly things from people.
There are only two horses on here (other then the OP's horse) that I would never guess were palomino (and the mare definitely looked it atleast up til 2), I would hate owning them and having to explain thier colors! It can be hard enough explaining their colors when they actually look like them! And that light palomino looks like a palomino to me (side note, but I say one on Craigslist not long ago that was almost the same shade, the ad said "golden palomino").