Hi Jan and Ben,
I hope I can be of some help here also. I can neither confirm or deny the report. Based on my research, it is certainly possible, like Ben said, that Walter Douglas was in the vicinity of boat D since he had just placed his wife and their maid Berthe in boat #2 just minutes before.
One needs to be careful about believing everything Mrs. Harris said about her experience.
Walter Lord, a good friend of Rene, was never convinced of her tale of leaving the Titanic all through the years he knew her. He jokingly commented on one occasion "that she must have thought that every man left on board stopped what they doing to carry her into the last boat because of her injured arm...."
In all fairness to Rene Harris, she was obviously suffering from the shock and exposure. Perhaps wishing to be of some comfort to the families of those that lost loved ones, she frequently wrote and claimed that various men, all valiant, put her into boat D. Names included Emil Brandeis, Col. Astor, Major Butt and of course, Walter Douglas, Edgar Meyer and her husband. It is impossible to say just where all these men were during the Titanic's final minutes but I think poor Mrs. Harris exaggerated a bit in naming so many men. Perhaps she was accurate, but, like Ben clearly pointed out, the 1932 Liberty magazine interview fails to mention them. Rene Harris wrote to the Brandeis family that Emil was in her cabin playing cards with she and Henry when the impact occured. She told Walter that only she and her husband were playing cards at that late hour ~ naturally so. She may have forgotten that Emil was hosting a party for department stores buyers, presumably in his cabin, on that fateful Sunday night.
As to whether or not Meyer, Douglas and Henry Harris headed toward the stern following Rene's departure, I can't say since I've never seen any other survivor make this claim. In some accounts, Rene stated that Emil Brandeis was with her husband near the end and that both stood there and watched her lifeboat drop to the sea. She went on to say that she NEVER saw them move from where they were standing and seemed to stick to that story more often that the rest.
Hope this helps.....
Regards,
Mike