I am not a lawyer but I did go to law school and took a keen interest in laws relating to aviation. I think I'd have a fun time picking apart your arguments, firstly on jurisdictional issues, but more so on substantive issues. thefreedictionary.com is not a legal resource nor would it hold any weight in a court.

Furthermore, BA is a UK entity and under UK contract law there has to be an offer, acceptance and then consideration.

BA is also governed by the rules of the CAA and not the DOT unless they are specified within a treaty between the UK and the US on a governmental level or through other forms of international law (ICAO/United Nations springs to mind).

I'm shocked to see that you are going to actually try and provoke the agent to refuse you entry.