It wasn’t about establishing Natural Born-ness, it was about getting the easiest path to citizenship. If she had to acknowledge he was born overseas, there’s a ton of paperwork involved. If she pretends he was born here in a “home birth process” the paperwork is minimal.
Do you think she knew about the paperwork? After all, she was only 18. On the other hand, its possible she and Barack Sr. had discussed it since he had international experience and hadn't split just yet.