If they do not treat fee waiver as bonus then what is the bonus they are referring to?
If one applied for this card and were to receive the "no bonus" pop-up, it is likely because AMEX created a one-size-fits-all pop-up to apply to any/all applications that meet their algorithm's criteria.
The fee waiver for this card is not a sign-up bonus, it's part of the T&C's that are applicable to the card.