Bulgari Hotels is partnered with Marriott...and utilize the Marriott booking engine, as a result. Do a search for Bulgari reservations on its bulgarihotels.com site and you'll see it looks exactly like the marriott.com reservation listing.
But when searching any location using Marriott.com, you'll never see a Bulgari property listed as an option, even when there is one. You must search from Bulgarihotels.com to book any Bulgari hotel.
I agree that this is a bait and switch. Marriott enjoys claiming it serves the luxury sector by "offering Bulgari" even though Bulgari hotels are not at all part of Marriott Rewards. It is considerably different from Ritz Carlton--where at least you can earn and use MR points for any RC stay, and where RC properties DO come up on a reservation search in locations that have a RC.