Even Picard acknowledges this in a season one episode "Justice".
I always fanwanked that as "Picard would have let almost anyone else die, but since he was responsible (? was he?) for Beverly's husbands death...he wasn't going to let her son die."
And re: Janeway and the PD, I hated that the one time she was willing to bend the PD (some Kazon ep) It all blew up in their faces and she got to say "See! SEE!!!"