I'd be a tad wary if it were me.

On ba.com, if, at check-in, you select a different seat to the one you selected prior to check-in opening, Manage My Booking still shows your pre-checkin seat.

After check-in opens, "control" of the flight moves to a different system and I'd be double checking that the call centre agent you spoke to is looking at that system, and not the same one Manage My Booking is looking at.

Of course, if this is a precursor to you getting an upgrade, you should be happy.

Do you have status with BA (or OneWorld) that allows seat pre-selection, or did you pay for seat selection?

Please let us know how it turns out.