It could have been Madelyn Dunham who, in the first week after BHO II was born, may have been aware of how easily HI birth and US citizenship could be established and filed a report of home birth not knowing when or if Stanley Ann would return from Kenya.
It seems to me that there some kind of serious falling out between Stanley Ann and her parents (beyond just getting away from BHO Sr) for her to have moved to Seattle with an infant at age 18 just one month after the birth. Most new mothers cling to their mothers and vice versa.
This falling out leave open the possibility that a parent or parents may have been taking actions that were not coordinated with their daughter.
She could have, but it would have been totally unnecessary under immigration law at the time. Since his mother was a US citizen, her grandson was eligible to receive US citizenship any time before his 18th birthday.
Now why would grandma commit purjury and risk jail time to obtain something that could be easily obtained legally?