I'm not a skeptic about this. The year 1912 was a vastly different era when duty, honor and chivalry still were the norm. And honesty was still the measure of a man. The recollections of the survivors all recount that the orchestra played to near the very end and I doubt that a lie was concocted.
From what I gather, one of the few men who didn't adhere to the "women and children first" mode of conduct was Bruce Ismay, chairman of the White Star line. He's generally painted as the villain in the narrative with some claiming he dressed in woman's clothing to secure a place in the lifeboats. Accounts vary on this point.
I think everyone in this thread will find In Search of Chivalry: Did it sink with the Titanic a worthwhile read. A key line in the article is: "74 percent of women lived while 80 percent of the men died."
You are correct that accounts vary widely on the conduct of Bruce Ismay, chairman of the White Star line.
It could be he was the villain as painted. It could also be that he merely grabbed whatever was available to get out and they looked like women's clothes.
Rumors were rife that he would try to flee from the rescue ships which brought the survivors into New York harbor, so much so that the coast card actually sent out patrol boats to escort them into the harbor and ensure that Ismay was available to testify at congressional hearings which opened within days of the disaster.