BB, if you think this is an explicit declaration that citizenship is not required, you've got some reading comprehension issues.
What do you think "not be used for purposes other than..." means in the paragraph you've pasted above? I'll answer for you: It means "can only be used".
So this means that they're saying that info provided for coverage will only be used for insurance-related questions or to verify eligibility for insurance including verification of immigration status.
The main purpose of what's written is they're saying that info supplied won't be used for other shit -- whether that shit is reporting illegals to La Migra or selling addresses to spammers.
The part that I've bolded strongly suggests that immigration status will be used to determine eligibility for insurance.
I realize your post is pretty old so I apologize if you already figured out you that your misreading caused you to take the opposite meaning from what was written.
Like the article I posted says: "The website goes on to explain that information shared with Obamacare cannot be shared with Immigration and Customs Enforcement (ICE). It does not explicitly warn that illegal aliens are ineligible."
So no, they are not ensuring that the applicants are not illegal aliens.