I wouldn't get too excited about this as it appears on the terms and conditions of some promotional offers, not the Terms and Conditions of Membership as you have cited. It could only possibly be an issue in an area like New York City where the Sheraton's of New York share the same in-house operations, including reservations and accounting.
I have no idea if this is how it is done in London.
Best regards,
William R. Sanders
Specialist, E-Communications Department
Starwood Hotels & Resorts Worldwide
[email protected]