I am not so sure Putin intends to "play ball", as much as play Erogan for a chump, and possibly subtlely set the stage for so much turmoil there there is a regime change in Turkey.
So much of this is about "What they DO, vs. What they SAY", kinda show me don't tell me, thus I expect something subtle from Putin, while something obvious is the smoke screen / red herring for it. I don't know if he KNOWS everything, but changes are he knows some stuff we don't. I think he gets pissed off in public and lets that display of anger possibly mislead people as to his directon, in other words he harnesses that public show of anger as a mis-direction play ( see Madden Football for the "Mis-Direction Pass".