Why would I know his daughter though?

Because she sings this CLASSIC!

She is a legend in her OWN RIGHT, regardless of who her father was.

Natalie has sold over 30 MILLION RECORDS WORLWIDE and won NINE GRAMMY AWARDS from TWENTY-ONE NOMINATIONS

Is she offended because they didn't ask her to perform it, or...?

Felt that one right in the childhood.

That's Nat King Cole's daughter

What? American Idol clearly tweeted that it was a cover from Natalie Cole
WTF is she talking about?

I recorded AI and they performed Inseperable literally 20 seconds after I read this thread so I was watching and they in no way said Jennifer Hudson originally recorded it. Natalie probably assumed that because the other duets were done with the original artists that American Idol thought/said it was originally recorded by JHud but they never explicitly said that.