I think you're right.
Alexei Volkov managed to make a run for it when he and other servants were lined up to be shot. This was out in the open, and I have a feeling that it was dark at the time. Also, I imagine the Bolsheviks would not have spent a huge amount of time and effort looking for him, as they would a member of the Imperial Family.
Ann
Right. If someone is fleet of foot and is in the middle of a wooded area it's actually a wise calculated decision to take off and run. You can probably outrun a guard/soldier weighed down by a weapon, ammo, etc. People also tend to be terrible shots firing while they are running. And with any luck even a spray of bullet fire coming from multiple guns might either miss you or hit tree trunks rather than body parts.
I remember seeing a History Channel program ("Modern marvels" or something similar) where they had two trained shots fire with rifles at objects moving in a serpentine motion from maybe 50-meters away. Needless to say it took a while before they connected with their targets...Bit of a further distance, yes, but these guys were excellent marksmen, and that was in the middle of a field!
Perhaps there is a certain sense of "even if I managed to escape wouldn't the honorable thing have been to die at their side", or "to run and live while your loved ones are getting mowed down is cowardice". Personally speaking I don't think I could leave the others behind as helpless victims, even though staying by their side would guarantee my own death.