I'm part of a group that owns & manages commercial real estate. For every property, there is at least one corporation (LLC) and sometimes 2 or 3. All together, we have well over 200 distinctly separate corporations, with the same president & treasurer, and support staff. If we could get a card for each corp, with a sign-up bonus, that would be millions of bonus miles.
My guess is someone like us tried to do this in the past, and that's why they link via SSN to prevent multiple sign-up bonuses.