I've seen offers that reward points for purchases, which the Blue Cash obviously cannot do. Other than that, offers seem to be randomly applied to different accounts, which is why having more cards gives a wider selection of Amex Offers. There doesn't seem to be any rhyme or reason for an offer to be targeted to one account as I have found out in the thread I started about authorized users
(my mom doesn't use her Amex at all but still gets good offers). Some do seem to have some reasoning, as my BCE always gets Whole Foods offers whenever they're available.
Before I learned it was fruitless to try to request certain offers, and that the Amex marketing department's allocation of offers was unchangeable, I called Amex to ask. The CSR (who was apparently fairly junior) took a few minutes to see if I could get a particular offer ($50 off $200+ at Brooks Brothers) duplicated on another card. When he came back, he told me that duplicating offers wasn't possible, but he also said he had learned that particular offer only went out to Platinum and PRG cards.
I only heard about one other person using that offer (people don't tend to talk about what they have no interest in), and it was also on that person's PRG.
So it's not definitive proof, but there is a reasonable basis for me to think some offers are limited to certain card products.