I agree that Marriott knows which card each person holds (or held previously). I do not understand why you think it would take an issuer 30 days to notify Marriott of a change. I doubt that the membership number is the only way that Marriott can look for a database match.
Chase will deny you welcome bonus if
- (1)are a current cardmember, or were a previous cardmember within the last 30 days, of Marriott Bonvoy™ American Express® Card (also known as The Starwood Preferred Guest® Credit Card from American Express);
- (2)are a current or previous cardmember of either Marriott Bonvoy Business™ American Express® Card (also known as The Starwood Preferred Guest® Business Credit Card from American Express) or Marriott Bonvoy Brilliant™ American Express® Card (also known as the Starwood Preferred Guest® American Express Luxury Card), and received a new cardmember bonus or upgrade bonus in the last 24 months; or
- (3)applied and were approved for Marriott Bonvoy Business™ American Express® Card (also known as The Starwood Preferred Guest® Business Credit Card from American Express) or Marriott Bonvoy Brilliant™ American Express® Card (also known as the Starwood Preferred Guest® American Express Luxury Card) within the last 90 days.
This means chase need to know if you have spg card for the past 30 days. I am not sure if someone cancel the spg card, amex will immediately notify marriott. And if you are approved for marriott brilliant card a few minutes before, they need to know that in order to deny you a bonus. I am not sure if this really works. But if this is the case amex will need to notify marriott immediately for them to deny you the bonus.
I also suspect marriott can use other information to search if you have it before. Other players applied for the marriott card without filling in the account numer, asked chase for the number they created and tried to login. When try to combine accounts, they only use name and email address. And in the online banking it seems they don't really have one's DOB. I doubt chase and amex are allow to give one's DOB and address to marriott. If one change the address on the existing account to a foreign country and use a different email for application, I doubt marriott can really identify them with the old account just by name.