I don’t think so because CS is I believe Christopher Steele and I don’t think Peter or Lisa were around the birth certificate thing.
Has something to do with meetings held in the UK, a lot if not all of those players were there at one time or another in the recent past.
I like your take better. Oh, well, maybe I’ll get one right one of these days!
maybe CS (Christopher Steele) helped hide the British Birth cert lo, all those years ago...