My interpretation of this message is that it only applies if the seat had been assigned free of charge by BA for some reason (e.g. for BA to pre-seat a non-status customer next to a Gold card holder travelling companion who could select seats for free). In this scenario the person who didn't (yet) qualify for free seating would be charged to change to a new self-selected seat.

The message is: "If you had previously been assigned seats free of charge, you will have to pay to change those seats. When you change one or more seats, you will be charged for all seats."

Having said that there does appear to be a bug where Bronze customers are being charged within the 7 day window.