Thanks for all responses, and yours.
As to the 1911, the original US manual on the 1911 cautioned against using the shooting method described.
And that cautioned was echoed in other manuals of that time. Here is a link to an article that has both the language and links to those manuals: http://www.pointshooting.com/1911.htm
The links and language on the 1911 are down a ways on the second part of the 1911 article.
In previewing/reviewing how the link and the link to the manual will work, I have found that since I found the original book and the contents for FREE and the link to it, it looks like someone has gummed up the works so all the contents are not available unless you buy the dang book from a source that wants to make a buck.
So, I will research my files, and if I can find a copy that I downloaded, which my OLD and fast fading memory says I did when it was available, I will put it up on my site, and add a link to it here.
As to the method of shooting one should use, per the studies of Police CQ combat, if you are going to be shot and/or killed in a pistol gunfight, there is a 90% chance it will happen at less than 15 feet.
Also, most all gunfights occur at less than 21 feet.
The reason is pistol accuracy in real life threat situations sucks (the Police hit rate in CQB is less than 20%), and that is because of the short length (sight radius), of pistols and because of the human response to CQ life threat situations. Also the link between range performance and street performance has not been established.
So it seems to me, that knowing how to shoot a pistol "accurately" without the use of the sights at CQ distances, would be good if you plan to survive a CQB encounter.
And most of the methods are not a bar to the use of the sights if you can see them and there is time to use them.