However, the trans worked fine when he test drove it, and when he drove it off the lot. Sure, there was a fault code identified, but the trans had all it's gears on a test drive.
I have 2 recommendations:
1) Call the dealer's General Manager. Not the sale rep, the GM. If the salesman represented the code as a simple $300 part, then as an agent for the dealership there might be something the dealership is responsible for. The sales rep is at best not knowledgable, or at worst a liar. Either way the GM should be the person with whom to talk. But know what you want to ask the GM to do. Personally, I'd want my money back.
2) Call an attorney. If the GM doesn't offer any satisfaction, hire a lawyer. Let the lawyer make the call to the GM.

As a couple of others have suggested, the OP already bought the X5, so now's not the time to criticize. Let's keep offering suggestions.

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'04 E53, 4.4 Sport
'97 E39 528i
'86 911 Carrera, track car
'96 BMW R1100R