Oh I'd feel terrible after. I'd go through a lot of things trying to justify it to myself. I'd wonder if I should have let him/her kill me, what their life could have been had they lived, etc. I don't think people that say "I'd let them kill me" are doing anything irrational. There's no way to know if I could even bring myself to even raise the gun, let alone shoot. But in terms of the most "rational" thought would be to put your own survival over the other person's , so I'd shoot the other person.
Of course the people saying it depends on their relationship to the other person have a significant point. That is certainly a factor as well...if it was someone I loved, I'd let myself die in a heartbeat. Thinking on my answer now, there is no way I'd kill my SO or a parent. If it were a friend or a relative outside of my immediate family I don't know how I'd react, as I love my friends, cousins, aunts, uncles, etc., but not in the way I love my parents or SO.