TS is not an advertised benefit, and nearly 100% of the online knowledge of BA's use of this module sits in this forum. So I'm a bit worried about Mr. 1A's mindset. The cabin crew tend to know very little about TS, other than over time some crew members have noticed that coincidentally Gold cardholders seems to have an empty space, but as far as I know, their job is to get boarding to happen swiftly and keep everyone safe, not get involved in status trade-offs between seemingly identical seats. Theoretical Seating is just that, a seating module. Along the way it does try to give the best seating options to those with shiny cards, but it also tries to keep couples and families together, avoid empty areas on the aircraft and so on. It is just about possible that 1A had purchased 1C too. I haven't seen this very often, I normally get row 1 and it's unusual for anyone else in CE to move in my experience, accepting that it does sometimes happen. I've also seen - more frequently - people voluntarily leave row 1 when they find out that they can't have their bags near them.

TS is used by a lot of airlines, though the parameters change significantly in terms of outcomes. Only on Lufthansa have I seen cabin crew try to enforce it.