Ethics and Legal Bargaining: When the Pre-Mediation Goes Up at the outset

It has happened to me twice in the past two weeks.  The Plaintiff's lawyer has sent a demand letter asking for settlement in a certain amount without the authorization of her client.  The response to the demand letter was a willingness to attend a mediation, which is then scheduled for 1-2 months after the demand was communicated.  Then when they arrive at mediation, the demand doubles or triples--simply so that they can get back to an ultimate settlement at very near that original demand.
While it may be a breach of ethics to make a demand to settle a case without specifically gaining the client's authority, the other challenge is that it creates  some awkward moments as the negotiation begins by going backwards, not forwards at the start of the mediation hearing for both client, mediator and the other side of the dispute.  For a mediator, it is a minefield when this discrepancy or intention is discovered for the first time in an initial session with Plaintiff and his counsel.  Where it occurs, I have had concerns about a breach of fiduciary duty to the client and may first discuss the issue privately with the Attorney and then, if they insist upon opening with a demand that is higher than their pre-mediation demand, unless there are new facts or circumstances, I will ask them to articulate the basis for that move directly to opposing counsel.
In both instances, simply walking gently down the path of understanding why the attorney made the initial demand and why the client insists upon starting at a higher demand may be all it takes to untangle the mess and advance the negotiation instead of jump backwards and head towards an impasse.  One of the best ways to avoid this is to question the lawyers before the mediation hearing as to any pre-mediation settlement dialogues and whether anything has changed to cause them to re-evaluate those numbers as a starting place.  They will likely reveal their issues during that pre-mediation conference call and allow you to break through this ethical minefield with all parties and their counsel in tact.
What do you do when there is this apparent reversal or re-appraisal at the mediation hearing?