They could easily have. Did you want the most recent Arpaio press conference carefully?
Saying he was a home birth at a friend's house doesn't fix the problem. If an investigator asked that other family or their neighbors, then it's the same problem as if they had asked the family with whom the Dunhams were living.
Remember, Grandma Toot when he was born did not know that one day historians and biographers might be asking questions.
Undoubtedly, they just wanted to avoid the red tape and hassles of raising their grandchild in the U.S. as a foreign citizen.
So, likely she just did the easiest thing and filled out the form saying the baby was born at home and sent it in.
You’re assuming that the mythological family in “Dreams” is real, for one thing. For another thing, if the mythological family in “Dreams” was real, it would have been simple to claim a birth at a friend’s house who did not exist, or who moved to the mainland or died later or was said to have died. You’re clutching at straws.
The point is that since a “fake but real” b.c. was easily obtained in HI, there was no need for the 0 team to make a recent forgery unless EVERYTHING on the b.c. is a lie.