No, what it shows is that people who call themselves Christians can be caught up in evil things, same as everyone else. To your point, humanity has some intrinsic moral understanding, certainly heavily configured by the surrounding society, for the survival of society. It’s not triggered necessarily by faith in some deity. Everyone is capable of good. Everyone is capable of evil.
If you want to take it a step farther and argue with someone pushing the “only Christians have a sense of morals” stupidity on their own turf, just point out that according to the Bible, we are made in God’s image, and since he has a sense of good and evil, therefore so do we. Even an evolution loving, abortion having, pot smoking, illegal immigrant might technically be created in God’s image. They have morals, and can do good or evil things.