Your CAG is determined by numerous teachers, not just your subject teacher. It goes through (or should go through) extensive moderation between a group of teachers, and the subject leader should approve that CAG. Finally, the head of centre (your principal/headteacher) and/or the leader of assessment in your school will give the final approval of the CAGs and send it off to the exam boards. So yes, higher ups can change your CAG if they believe it isn't right, but only before the CAG is actually sent off.
IF there is any issue with your CAG on or after results day, you can appeal due to a technical issue made by staff at the school who may have incorrectly calculated a CAG, or you can appeal if you believe you have been discriminated against. Those are the only times your CAG will change post-results day, and teachers can't just change it willy-nilly. They have to go through the CAG process outlined above just for you again.