The correlation comes from the fact that you cannot shoot unless you have possession and that once in possession of the puck the object is to score. But this too cannot happen without a shot attempt. In the end though it is as you suggest an imperfect measure.
I understand the (imperfect) logic completely. My point is the stat abuses the notion that all possession is equal and all shots are equal, or that these things balance out. It would have said that our mid-nineties dump and chase, crash the net, high shot volume and decent puck recovery teams were better "possession" teams than the great puck moving teams with relatively lower shot volume opponents we looked up at every year at the top of the standings.
I'm sure we've all played on, low talent teams that took every shot they could and jammed the front of the net... where their only true skill was being a collective group of puck-hounds. These were not "possession" teams, corsi be damned.
If people wanted to say the stat was a proxy for "puck recovery" ( =/= possession), I suppose I'd be happier.
Full disclosure: my bias comes from currently playing goal on a team that fires random shots from everywhere (check that... from the perimeter), with no traffic, and gives up 6 breakaways and 12 two-on-ones per game. They ROCK from a corsi perspective and are (all too often) the epitome of the strategy employed by an otherwise-overmatched team of hard-working puck recoverers.
