I do think Jang Uk giving Mu-deok the jade eggs in Ep 6 saved their lives, but not because Mu-deok would have handed him over without a second thought, but because she would have regretted it too late and Jang Uk wouldn't have been able to save himself or her.
She was already trying to convince herself that she was right as they walked over. She was going to crack at some point and try to save Uk, but we see how ineffective she is without powers and Uk would die trying to save them both.















