In your shoes, that's the point *I* would emphasize with United customer service. The flight *MAY* have flown with weight and balance listed as the reason for IDB. Regardless, I would be making the point that *I* was informed I was IDB for an oversale situation and I want compensation appropriate with that.

Honestly when I first read your OP I saw the weight and balance response and didn't really notice you'd said oversold. I suspect customer service is missing that also - either as an honest oversight/miscommunication or perhaps because the flight records show it as w&b. I would be very explicit with CS that you were told you were IDB for oversale and ask specifically whether the records show you as IDB for W&B. Assuming they come back and say "W&B" then I'd respond along the lines of: "Now it seems we have a real problem. I was explicitly told that I was being denied boarding due to an oversale situation, and you're telling me the flight was recorded as having weight and balance issues. I don't know whether someone lied or an honest mistake was made, but I need to be compensated for the situation as it was described to me. I would be satisfied with <insert what you want here> as reasonable compensation for being denied boarding regardless of what the actual situation might turn out to be. If that is not possible then we need to find out whether the gate agent denying my boarding lied to me or on the paperwork showing the flight status. Given the obvious seriousness of the weight and balance issue, I see no way to achieve that other than to work through the DOT and report the incident to them both as a violation of the denied boarding rules in <whatever section you quoted before> and as a fraudulent flight record <ideally find out what rule they would be violating and refer to that here>."

Richard

Lots of obvious disclaimers here - both about legalities and non-lawyerness as well as the issues around ultimatums, etc...