I, too, prefer historical accuracy. However, the story of Mary Stuart has long been influenced by romantic mythology. Therefore, as long as the screenwriter did not alter the basic factual outline of his subject's life and the outcome of her long political quest, I did not--and do not--see a problem with a "secret meeting" between Mary Stuart and Elizabeth Tudor in that particular film. The romantic tone of
Mary Queen of Scots is well-established within the first few scenes; just by virtue of being in a theater we know we are watching an interpretation of Mary's actual life, which was for the most part dreary and very sad.
Mary and Elizabeth have been portrayed on stage and screen by many distinguished actresses, and many highly competent dramatists have written stage plays and screenplays based on their lives. Drama is just that: A heightened portrayal of reality. While I believe that dramatists should not take gross liberties with historical events and the persons who participated in and/or shaped these historical events, I realize there is also a need to shape a story into an experience that will work within a dramatic framework.
The difference, I think, can be shown in comparing
Rasputin and the Empress to
Nicholas and Alexandra. Allowing for the considerable gap in time and therefore technical quality, I continue to maintain that the latter is far superior to the former because it makes a sincere attempt to be accurate to the spirit and tone of the basic story. On the other hand,
Rasputin and the Empress has a slapdash look to it. The script is generally ludicrous and the characterizations generally out of sync with what we have read in many, many memoirs.
Nicholas and Alexandra--for whatever its faults--is based on a well-researched biography, and it is obvious that a conscious and conscientious effort has been made to adhere to that primary source.
While
Mary, Queen of Scots is far from my favorite fiilm re: royals and, yes, features that highly questionable meeting between the royal cousins, I would recommend it--with a few cautionary comments!

--to anyone interested in the story of Mary Stuart.