I don't know the answer but I just wanted to point out the contradiction in Pub 972. For $1,500 more in credit, I'd be inclined to see if they can get a SSN based on the birth certificate. Sounds stupid but I'd file it under "unintended consequences." What a sad situation.
I would tend to interpret 24(e) to be absolute:
https://www.law.cornell.edu/uscode/text/26/24#eRick
