I always wondered about this. How for example FDX operated an intra euro flight to and from DUB on a purple tail (I believe they run a EIDW-EGSS-LFPG). I had assumed that brown is carrying local volume from EIDW-EINN to justify the use of Star. However, ABX, US registered airline, does not have cabotage rights within Ireland. So either Star has arranged for local volume to move another way or brown has never moved volume locally on that leg (similar to moving LEBL-LEVC or LIPZ-LIRA volume but not on a browntail).
Best I can read (rather quickly mind you) the latest EU-USA Air Transport Agreement of 30 April 2007 Article 3:
(c) the right to perform international air transportation between points on the following routes:
(i) for airlines of the United States (hereinafter "U.S. airlines"), from points behind the United States via the United States and intermediate points to any point or points in any Member State or States and beyond; and for all‑cargo service, between any Member State and any point or points (including in any other Member States);
(ii) for airlines of the European Community and its Member States (hereinafter "Community airlines"), from points behind the Member States via the Member States and intermediate points to any point or points in the United States and beyond; for all‑cargo service, between the United States and any point or points; and, for combination services, between any point or points in the United States and any point or points in any member of the European Common Aviation Area (hereinafter the "ECAA") as of the date of signature of this Agreement; and
There may very well be some extraneous agreements and treaties involved that I am not aware (some one with more lawyers, time, and inclination should look at it), but experience says that if one airplane with a US flag on the tail can operate it, then any other can... regardless of what paint scheme is on the rest of the plane.
[small point, brown does not believe in painting the US flag on its airplanes... unlike EVERY other major(and most regional) US carriers.... makes you wonder if they're proud to be Americans?]