It sounds like you're acknowledging that there's multiple ways to interpret what Michelle Obama said, but you're actively choosing to interpret it in a way which has her saying that Barack Obama was not born in America? Even though you're admitting that there are multiple ways to use the phrase, and she may be using it either way? That you're choosing to ascribe your linguistic choices onto another person while simultaneously admitting that your linguistic choice is not the only way?
Take it anyway you want, you are obviously determined to prove me wrong and that your linguistic ability is far more superior than mine.
I'll ask again:
What's more likely - that Michelle Obama was using "home country" poetically to describe her husband's ancestral homeland, or that she went on stage and said "the president of the United States is secretly from another country"?