When is an orle not an orle

On Saturday I gave a tour of the heraldry in Trinity College Oxford to some members of the White Lion Society. This was very agreeable, and we had some lively discussion about the interesting heraldry in the hall.  This however was as nothing to that which erupted over the arms of Balliol College, which adjoins the grounds of Trinity.  The arms of Balliol are those of the founders John and Devorgilla de Balliol, the parents of the future King John I of Scots. Significantly Devorgilla, as heiress of Galloway, has precedence over her husband's arms, gules and orle argent.  This what the college says about their arms on their website.  Arising from the way the arms were depicted in stone and on the college flag which fluttered overhead there was an amicable, but nonetheless heated, discussion amongst some of the members as to when is an orle not an orle, and when does it become a tressure... at one point I thought I ought to suggest sending in an heraldic peace-keeping force. If you have views on the status of an orle, please feel free to comment, but I will not commit to adjudicating.