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The Levin-Grue auction

We are told that Mr Levin (West) and Mr Grue (East) bid as follows:

West
K92
KQJ95
AQJ75
East
AQJ1065
A107
Q95
K
W
N
E
S
 
P
1
P
1
P
3
P
4
P
4
X
P
P
4N
P
5
P
7
P
7N
P
?

Perhaps it is my lack of familiarity with their methods, but I find this a bit strange.

The 1-1 start is normal enough (though some would respond 2 if systemically allowable).  I can understand 2 or 3 as a rebid with the West cards, but 3 looks to be somewhat of a distortion with moderate three card support and an excellent club suit: 6 could be the right contract facing as little as Axxx 10x xxx Kxxx (not that it is likely to be bid).

Over 3, East cue bid 4.  Maybe this was defined as a serious slam try, maybe not (parenthetically, if West is going to raise to 3 with Kxx, East might well wish to bid 3NT non-forcing).  West responded 4, North doubled and East passed, which denied first round diamond control.  West now took over with RKCB and, having heard of two aces plus the queen of trumps, bid 7.

West limited his hand with 3 (not a particularly accurate limitation in my view) and, in the light of a below-game slam try from East, decided that a grand slam in spades was appropriate.  That is, with no further indication at all as to whether East was interested in a small slam or a grand slam, he took it upon himself to bid the grand.  Note that this hand took place during the "first final session", not right at the end of the event when a desperate throw of the dice might seem attractive.

Could not West have held AQxx (with compensating high cards elsewhere)?  Or could he not have held roughly the hand that he did but with Axxxxx in spades and have shown that he had Q since he "knew" that there was a ten-card fit?

Can someone explain what I am missing here.

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