I did book the flight as a test, and YES the bags were included when I went to the British Airways Manage Booking Page. As Chase says, they don't guarantee it, but it's accurate in at least my case when it says 1st bag is free, so I'd imagine it therefore is usually accurate, but clearly Chase won't stand by it if you get hosed. Best to check with airline booking confirmation reference within 24 hours of booking with Chase to confirm if bags are included.