I can't think of any reason for the Doctor to have lied. It seems like there is going to be a reason but they don't do anything with it so I think they had to have that scene so they could never talk about the baby again.
Why should Cullah bother with this child if he has any doubts? Why would he not have doubts, he's realized Seska was manipulative.
Really my point is there are a hundred ways this baby's life could be a crapfest aside from the assumed crapfest that is normal Kazon life. And Janeway did not care. Once it was no longer Chak's she lost all investment in its well being.