A similar recent promotion may shed some light on the proper interpretation of the rules for this one. Remember a year or two ago, Marriott offered bonus points for stays paid with AMEX? I got quite a few points under that promotion. But in many cases, I paid for part of the stay using Bonus Bucks (or the equivalent Marriott Cheques). Nevertheless, I got the full bonus on my entire bill, not just the part charged to AMEX. Marriott's systems recorded the stay as AMEX-paid, even though it was not 100% AMEX-paid. The analogy to this latest promotion is pretty obvious.
Bruce