Mia, I had the same feeling you did...
I think the phrasing leaves open the possibility of using another card:
"Check out with your Chase card and your extra points will automatically appear on your statement."
Also, the transition page when navigating from Chase to Kohls includes the following language:
"Please note these terms & conditions: Special increased earnings now through 3/31/2012! Not eligible on gift cards. Eligibility calculated on final sales total (after discounts or promotions are deducted from purchase price, including Kohl's Cash). Not eligible on Kohl's credit card sales made with coupon codes that are higher than 15%."
The part about Kohls credit card sales with specific coupon codes suggest to me that if you do not use coupon codes over 15%, you can use your Kohls credit card and get points.
The CSR I spoke with verged on rude about this; however. She was insistent that those were KOHLS terms and conditions, not Chase's, and that they had nothing to do with Chase. She said the "check out with your chase card" is all that matters.
How do others interpret that language on the Kohl's transition page?
Anita