A meconium spill is dangerous because a baby might get it in their airway and aspirate it but obviously your brother did not aspirate it. It is a common problem though and doctors/nurses suction out the baby's mouth immediately when there's a spill to be sure they do not breathe it in. I think the doctor was speaking in terms of, "if he aspirates it he could die. . ." not that he could die just because there was a spill.

I don't know where the story of the other woman claiming your brother was her child came from, that would not be something told out straightforward to your mother by anyone in authority and it could be mixed up (someone teasing because your brother was so cute or a passing comment only partly heard) or just a story someone made up, etc. but with footprints and all the other registering they do of babies (and I was born in 1950 and have my medical records with prints :-) I think it is very rare that babies get permanently mixed up.