High forgiveness, high precision = tight grouping around the target (accurate & consistent)
High forgiveness, low precision = loose grouping around the target (accurate but inconsistent)
Low forgiveness, high precision = tight grouping, off target and short (inaccurate but consistent)
Low forgiveness, low precision = loose grouping, off target and short (inaccurate & inconsistent)
I have a slightly different interpretation, but only because we need to make a distinction between accuracy and precision. You can be precise without being accurate.
As you said, precision determines the tightness of a player's shot results. However, that just means your shots will always be grouped together
tightly, but doesn't exclude the possibility that those shots are
grouped together tightly in the water hazard. Accuracy in this instance is the combined result of forgiveness, precision and the player's ability to correctly calculate and execute their shots.
Low precision = Shots are in the extreme precision areas (farthest from center) almost as frequently as they are around the center of the precision area and in between. Loose grouping.
High precision = Shots are mostly around the center of the precision area, with a lower frequency of shots in the more extreme areas of precision. Tighter grouping.
High forgiveness = Nerfs the mishits to a certain degree, so as to keep the precision area close to the intended distance and direction, relative to the amount you mishit.
Low forgiveness = Less or no nerf on mishits, which can cause the precision area to stray pretty far from the intended distance and direction, relative to the amount you mishit.
I'd also like to add that the precision area is not quite a circle (though it may have been illustrated that way by the OP for simplicity's sake). The distribution pattern is more akin to a diamond that is stretched somewhat vertically. Kinda like this, but not quite so "pointy".
In other words, the amount of potential standard deviation, sans wind, is slightly greater short to long than it is left to right. Putters are basically the same, which someone did a great job of illustrating in another thread (I forget who did that).
This would correctly represent an assertion that good golfers are more likely to miss "excellent" shots long or short by greater margins than they are left or right. You can see this in game as well. With a ding you can easily be 10% long or short given any distance, but you don't miss wide by that much (again, sans wind) unless you mishit the ball.
Forgiveness is essentially what keeps mishits in check and prevents your shots from grouping tightly in the water hazard. Forgiveness works to keep the precision diamond close to where you aimed. Mishits work to relocate the precision diamond, generally biased to the short side, by an ever increasing factor. For example, you don't miss your 3-Iron by 10 pixels left or right and end up with 20 yards of extra carry. However, it is possible to end up long with a 1 or 2 pixel miss. The greater the mishit the more the bias to the short side.
Here's how I think a 3rd grader would illustrate this:
This a flat, windless golf course with utopia-like conditions. Perspective is set from the blue tees, the golfer is aiming directly at the cup. Drawing is not intended to be perfectly scaled, representative of any existing club set, or good.
There's our precision diamond (same size for everyone). Hit the ding 100 times on a correctly calculated shot with a high-precision club, and your 100 shots will mostly be grouped tightly around the center point of the diamond. You'll have some average deviations (2-4yds), and very few results in the extreme areas of precision (5-8yds). Hit the ding 100 times with low precision and you'll be scattered about the diamond with a very loose center grouping.
The hollow purple diamond-ish shape on the illustration is the area provided by your club's forgiveness rating. The higher the club forgiveness the smaller the purple area which helps to keep your mishits closer to the intended target.
Purple also represents all potential spots where the center of the precision diamond could end up on any given mishit that occurs in the light blue part of the swing meter. The higher the degree of the mishit, the more likely your precision diamond will get shifted to the far left, right and/or short extremes of the purple area. Miss the ding in the dark blue part of the swing meter and your precision diamond will be exponentially stranded somewhere within the entire red area, relative to how much you missed.
The randomness we experience (deviation) is the fact that any shot could end up anywhere in that black diamond area, regardless of mishit or ding. However, where that black diamond gets relocated is based on the combination of club forgiveness and the severity of a mishit. High club precision does not shrink the diamond, it just decreases the likelihood that you'll end up in the more extreme regions of it. Both WGT starters and the best clubs available can deviate 7-8 yards left or right in the extreme cases, but the better clubs do it much less often.
After you hit the ball it factors in all the external shot data (such as the wind) with your swing result and pinpoints an EXACT location. However, that exact location is just where the center of the precision diamond goes. You are then subject to actually landing somewhere within that diamond based on your club precision, and then subject to whatever happens on the ground once it lands.
This is seen in game as well. It is possible to mishit a shot that, based on the initial calculation, should put you 6-7 yards left of the flag. The diamond is centered there, and then you end up actually landing in the moderate right portion of the diamond's new location, thus correcting 4 yards of your 6 yard mishit. Then once you hit the green and get a bounce to the right suddenly you are 4 feet from the pin.
Deviations can work against you, sometimes harshly, but they are also corrective at times, giving you better than you deserve as a result. Everyone has shots or putts that have absolutely no business finding the hole, but somehow they find it anyway. Those are the good, corrective deviations, as it were.
Kudos to the OP. Fantastically illustrated and presented.
So, let's go get a beer. I know a place...