I don’t thinking Casual PvP battles show up in your opponent’s Battle Log – each of those battles has a PvP Score change associated with them, and iirc CPvP has no effect on PvP Score.
I definitely agree with the rest of what you said, though!!
(See my video in the “PvP Diversity Issues” thread:
where I fight Bernice 13 or so times in that kind of time frame by pressing refresh a couple of times after each battle.)