Mistake, or brilliance?

I recently read a bridge blog in which the author did an exhaustive analysis of 100 hands he played and then gave a statistical summary of mistakes made by himself, opponents, and his partner, and the imps they cost. While I agree that it is a good idea to analyze your own play for mistakes, I think it is not necessarily a good idea to look at your opponents or partner unless you know you are significantly better - they may have chosen their line of play based on an inference you didn't catch.

A hand I played on BBO provides an example of this. I was called into play as a sub in a teams game, and have the pleasure of defending a 3N contract:

East
KJ92
KQ102
42
Q63
South
Q85
8653
A1073
K2
W
N
E
S
P
P
P
2NT
P
3NT
P
P
P

Partner led the 4, upon which dummy played low.

My own thoughts on this hand were as follows: Dummy has 11 HCP, I have 9, declarer has 20, that leaves nothing for partner. Wait a minute, that low heart lead is funny - even if partner is leading from a 3 card suit, I wouldn't expect him to lead low. Could it be a singleton? Maybe, but I don't think so - a partner astute enough to try and find his partner will also be astute enough to notice that I passed 3rd seat white, so I don't have anything I'm dying for him to hit. What's left?

My best guess is that declarer is 4-1-4-4 with the stiff A, and that partner has the J. That's what I'll play for until I find a reason to play for something else. If I'm right, declarer has all of the rest of the HCP.

Having worked that out, I decide to follow with the 3, and declarer wins the ace. You can see the complete hands played out below:

Notice that when I won the Q I returned the 3rd so that declarer has to do her own work. Ducking two diamonds appears right, too, for the same reason (and to maintain the illusion of communications with partner). In the end game that developed, I had it all worked out: I was going to duck smoothly with the K, and my opponent would take her safe 9th trick with the A. Imagine my shock when my expert opponent (who has won multiple national titles) paused to think, and then finessed anyway!

If you were doing a strict analysis of the play, you might be tempted to say that my opponent made a mistake in the play - like an unnamed player watching the table subsequently did. After all, if my partner had the K, then we could theoretically win that trick, the J, and 2 tricks to go with the Q I had already won, putting her down in a cold contract. That's the superficial analysis which would hold if declarer was a bad player, but this was not a bad player - this was a player who competes at the highest levels of bridge. When a player like that makes an apparent mistake, I want to look deeper.

In this case, I think my line of defense tipped declarer off that I was looking at all of the HCP. Returning the spade instead of a more natural looking diamond must have given declarer the inference that I was looking to be as passive as possible because I knew the hand, something that was most likely to be true if I knew partner had a yarb. Declarer must have confirmed that inference from my subsequent diamond ducks, and decided that my defence was extremely unlikely unless I had the K - then trusted her judgment enough to decide that it was worth risking 13 imps to avoid losing 2 against the presumed 650 from playing 4 spades in the other room. Bravo to my opponent, I would not have had the courage to back my judgment that far - which would have been my mistake.