The answer is no unfortunately. You are all correct though. Unfortunately the terms for this vendor are very clear:
Not eligible on Purchase Plans including, but not limited to Employee Purchase, Shareholder, Member Purchase, Friends & Family, Contractor Purchase, Corporate Purchase, Lenovo VISA Cardholder Program, or Student & Alumni, and purchases made through Office Depot. Not eligible on Bill Me Later sales. Lenovo Outlet Items are not eligible. Lenovo.com has a Limit of 5 items per customer on any order. Effective May 1, 2016, Lenovo will not be paying out on orders that have more than 5 items per order. Not eligible on Moto branded phones, Motorola products, gift wrapping, and orders placed for reselling purposes. Not eligible on purchases made with coupon or discount codes that are not found on this site. Not eligible on gift cards, gift certificates or any other similar cash equivalents.
So since I've got 22 items in my cart it's a no-go. I probably could have tried splitting it into 6 orders but no.