The only problem I see with that story is that in 1971 children did not need a Social Security Number. I got my SSN in 1967 when I applied for a summer job at 16.
Catholic Social Services of Connecticut maintained legal custody of BHO II until he turned 18. Madelyn Payne Dunham, Obama’s grandmother, was appointed his guardian during this time.
When Obama was 15 or 16, Catholic Social Services applied for an SSN on Obama’s behalf and used their Connecticut address as the return address on the SSN application. Consequently, Obama has a prefix SSN indicating a Connecticut number.