I was Survivor/Bodyguard/Doctor, I vested/self-healed and was transported, and I died! Why?
When you perform any action on yourself, your character will visit itself. So, if you are transported with someone else, you will no longer be visiting yourself, and therefore not protecting yourself.
This has not been true since self-heals and self-vesting were made astral. I don't believe it was ever true of Survivor, as he still vested even if made to visit another person (before the change).