So you tell me. Do they have the power to do that? If so, it seems like they would be able to sign people up to any promotions as they see fit!
There has been 200+ pages of discussion on this point. Your suggested starting point is there.
After trawling through that you'll probably realise that there are a number of different thoughts on the topic and no simple anwer to the question you pose. That's the thing about law - it is rarely clear.
Relevant considerations are that the bonus promo T&Cs said that they were subject to the MR T&Cs. The MR T&Cs suggest that 1) those T&Cs can be amended unilaterally without notice and 2) that there was provision to allow AMEX to deal with you how it sees fit if it considers there has been fraud or abuse (this is from memory, but I think cl 14).
The bonus promo terms were very light and didn't clarify whether all three promos could be signed up for. One would have to think, reasonably, that it was clearly not the intention of AMEX that a person who put through 20 transactions in a month was to receive 4 x 5K (5t/5k) plus 2 x 5k (10/5k) plus 1 x 10k (20t/10k). Instead, one would reasonably think that each transaction would only count towards one bonus promo only, whatever that promo be.
Some people have thought about whether there has been an offer/acceptance or consideration and whether a contract has been formed. For my part, I don't think this is an issue. On a narrow reading, the terms of the contract would allow AMEX to make pretty much any changes it chose to. In my view, this is practically settled and not in issue. For me, the relevant question is can this be done having regard to the consumer protection laws? It has been said plenty of times before: just because a contract says something doesn't mean it is enforceable and doesn't mean that it isn't in breach of legislation.
The Trade Practices Act generally provides consumer protection, although does not apply to financial services. The ASIC Act is the relevant legislation in this regard and, in particular, Part 4 Subdivision D (s12DA, for example).
I suggest you read the Consumer Protection sections of the ASIC Act and form your own views as to whether the action that AMEX has taken is in breach of those legislative boundaries. As it applies to me, the conduct of AMEX seems to have breached the ASIC Act. However, I don't determine these things and I also don't know all the circumstances that apply to you.