I think the shots performance analysis is probably reverse causal. I.e. he got more shots because he was playing well rather than he plays better when he gets more shots.
I think you're first point is correct in the statement "he got more shots because he was playing (better) rather than he play(ed) better when he gets more shots," but take issue with the "when," since it implies my argument stated that 12 shots guaranteed him success, which was not my argument. My post was a historical reference showing his success with 12 shot attempts, that's all. But if we take the "rather" out of your statement, I think the data supports both points:
1.He got more shots because he played better.
2. He played better when he got more shots.
I think they inform each other, not cancel each other out.
For instance, basketball is a game of possessions, and there is only so much shooting to be had by each team. If there are players on a team who aren't keen on passing to you, because they'd rather shoot themselves, or the coach told them to pass to someone else, how good you are doesn't really matter. Another factor to consider is how one's confidence is constructed. For most people, it is built via history, by past opportunities to manifest ones' abilities, they are more likely to believe in them, and thus act on them in the future. It's the old adage "practice makes perfect," but if there are elements (players/coaches/possessions), preventing one from getting that practice, one wouldn't be confident to shoot more, thus one's teammates could sense a lack of confidence and not pass to them. It's a catch-22.
At any rate, here is some more data that could be bent to support either/ both claims:
Al Jefferson averaged 15.8 shot attempts last season, scoring 17.8 PTS . These were his attempt numbers/production in the games where Marvin shot the ball 12 times:
10/31 vs Dallas
Jefferson went 4-11 Scoring 12 PTS
11/23 vs SAC
Jefferson shot 8-14 Scoring 19 PTS
12/22 vs MIA
Jefferson shot 2-8 scoring 6 PTS
2/2 vs POR
Jefferson shot 6-13 scoring 12 PTS
In the games where Marvin shot the ball 12 times, Al didn't shoot his season average of 15.8 attempts. Al only scored his season average in one game where Marvin shot 12 times (vs SAC Al had 19).
Mo Williams averaged 11.6 attempts, scoring 12. 9 PPG. Here's how he fared in those same games:
10/31 vs Dallas
Mo shot 7-16 for 21 PTS (good job Trey! I mean Mo!).
11/23 vs SAC
Mo shot 0-1, scoring 0 PTS.
12/22 vs MIA
Mo shot 2-3, scoring 5 PTS (only played 16 minutes, and got injured).
2/2 vs POR
Mo shot 0-0, scoring 0 PTS (injured)
The data shows us that Al took less shots in all 4 games, and only met/excelled his season average in one of those games. Mo shot less than his season average in 3 of those 4 games (by a lot less in 3 of them), and only met/excelled his season average in one game. With the data, I assume that with Mo and Al shooting less, there were more shots for Marv (so it was an issue of posessions), and when he's taken more shots, he's capitalized on those opportunities.
*all data taken from ESPN Game Logs.