No what you were saying was that if MAN refused to serve BA it would be in breach of the free travel agreements which apply only to governments. There are probably other restrictions in terms of commercial law but the particular rules you mentioned with regard to intra-union travel don't apply to that situation, simply because they aren't restricting intra-EU travel (because they don't have the power to do that). I hope I'm being clear I have a tendency to talk around the issue. Put simply, companies can't be reprimanded under free travel agreements, EU commercial law is another matter of which I have zero knowledge.
Like I said, I was under the impression you were speaking of free travel agreements which ban any restriction of EU travel by goverments rather than free trade agreements. I hope you see my misunderstanding.