Yes, what I wrote was a drastic oversimplification. But I was talking particularly in the context of holds. In a B737, if you take HDG SEL and 30 degrees of bank, you will do a 30 degree banked turn onto a heading. If you stay in LNAV, then it will fly round its nice tidy racetrack, with (in some winds) as little as 5 degrees of bank to keep it sweet. In an A320, you may be turning back to the hold with a 30 degree turn in NAV (which a B737 will rarely use, as it works out its nice tidy racetracks). If you pull HDG, it will slope it off to 25 degrees. And if there's a way to override this 25 degree turn in HDG at that level, with no other modes engaged, then I don't know what it is. Yes, a little knowledge is a dangerous thing. Perhaps you might like to explain how that can be achieved then?
The point I was making is that pulling HDG in an A320 will not necessarily improve your turn. In a B737, selecting HDG SEL and a 30 degree AOB will give you the best turn. This has a bearing if you are told to "tighten up the turn" - a subject which is related.
I would have written a full behavioural explanation of the autoflight systems of the B737 and the A320, but I thought it might cause people's optic nerves to leap down their throats and strangle them before they died a horrible death of boredom.
The radio calls are not standard. They are all used, and are all precise instructions. I don't know to what extent HD or others were aware of the variations used by other people. I guess the LATCC crowd are pretty aware. Others might not know all the details of this argument but might be interested.