Idk, the whole party finder race to be the first sounds off to me though. Like you could do your research and be prepared, and be the first to trade the Gil, but once that's done it would be a race to be first to the market to buy the plot because unlike with a private exchange, everyone who looks at PF at that time knows that plot is about to be relinquished right then.

Outside of that, you're not buying a house from that player, you're only paying them to free up the plot as there isn't currently a way to directly transfer a house from one character to another outside of leadership of an FC with housing being passed to you. But if he never explicitly stated that until after accepting the Gil you may have grounds to stand on but it would ultimately depend on the gm's decision since SE have been very clear on how housing can be obtained even if the seller wasn't. Good luck on that, but you're right, it does pay to do research.