“AMEX Canada Card”? How many other countries have AMEX Country Cards? Maybe someone should start a new company in Canada and call it “CANEX”. Then USA citizens can get a CANEX American Card.
I don't know why you think it is so odd. It's pretty standard that US corporations operating outside the US have local subsidiaries due to local regulations. US rules, regulations, and standards have no application outside of the USA. McDonald's Canada, as well as in other countries, is a separate entity, even if it is ultimately owned by the US parent. It also often means the benefits or menus are unique to the particular country.
Just like VISA and MasterCard, for the card to be issued in Canada under federal banking regulations here, it must be issued by a Canadian bank. Amex Bank of Canada is the issuer for Canadian residents. There may also be separate affinity cards issued within Canada as well. It is a subsidiary of American Express (US). It works much the same in other countries, too, such as the UK and Europe. I wouldn't be eligible for a US Amex, since I am not an American resident and have no credit rating in the USA.
By the same token, if there was such a thing as a CANEX card, you wouldn't normally be eligible as an American resident, unless you have property here or some other relationship.