This idea that the vessel "mistaken" for Californian "steamed away", and therefore NOT the Californian has always intrigued me.
Having served on the bridge of US Navy ships for 20 years, it occurs to me that what might be actually "mistaken" is the appearance of "steaming away".
Californian's navigation lights (with the exception of white masthead lights) and whatever cabin light showing from the hull and superstructure are relatively low... perhaps no higher than 30-40 feet above the water.
These lights would be visible from a distance of 6 or so miles to someone in the water (i.e. on the horizon).
The same measurement for Titanic (nav and most cabin light), at about 60 feet, would be about 9 miles.
Combined, this means an observer on Titanic's or California's bridge could see the other and possibly (but not likely) determine "target angle" (the direction the other is pointed) at about 15 miles, masthead lights notwithstanding.
The white masthead lights MIGHT be seen from an even further distance, but without being able to see the red or green sidelights, no determination of target angle would be possible. In fact, the masthead lights COULD be mistaken for the white stern light.
I have no idea at what range the masthead lights could be seen (their "luminosity"), but I doubt it would be much more than 10-15 miles...in fact, modern-day regulations stipulate that masthead lights need be visible no more than 6 nm, 3 nm for stern light. This minimum is based on BOTH strength of the light and height above the water. It is possible to greatly increase the visibility range by raising the light, which masthead lights naturally are.
Suffice it to say that it is no surprise that a vessel could be seen clearly at a range of 10-15 miles.
There are too many references to seeing a vessel at about 10 miles for this to be fantasy or a mistake.
With all this in mind, I can easily see why the "mystery vessel" (actually Californian)was perceived to be "steaming away"... as Titanic's bridge got lower and lower, and as observers themselves entered the boats and eventually the water.
First, whatever hull lights one might see of the other would "disappear"... then, the side lights and superstructure lights... and then the foremast light, and finally the mainmast light... looking at last no different than a stern light.
The "mystery vessel" would appear to be moving away, even from the time of collision to the time of launching the boats (over an hour), by which time Titanic had already gone down by the head by 30 feet or so, the bridge lower to the water by at least 20.
This "dip" in observers' height during this hour alone would give the impression that the mystery vessel was 2 miles further away.
By the time an observer in the first boat was lowered from the boat deck to the water... a further 40-50 feet... the observer would be near the extremes of visibility for all but the masthead light(s)... those highest and most powerful...and possibly mistaking what light they saw as a stern light of a vessel steaming off.
This would put the mystery vessel at anywhere from 6 nm to perhaps 10 or so nm away.
It's entirely possible that the impression of the mystery vessel/Californian to be steaming away is based entirely on this change of perspective.
Even the watch on Californian's bridge is said to have had the impression of Titanic steaming away... by simply reversing the problem.