So by your rationale, it would be OK for say BP to come into the US, buy up every oil producer, and have a monopoly on the market simply because they are not a US company? If a company operates in US markets, they are subject to US law.

The BA-AA issue stems from the fact that the US and UK do not have on open skies agreement. Their air treaty limits LHR to US slots to 4 airlines (BA, VS, AA, UA). If BA and AA could essentially combine their trans-Atlantic routes, they would probably have 75% of the slots going across and probably have strong monopoly pricing powers.