Also, I would argue that some of Germany rearmement might have been unknown to Western intelligence. I remember distinctly a doc mentioning German paratroopers training in the USSR (post Pact, of course), obviously to hide it. Doesn't really detract from the overall point.
Germany had been training in the Soviet Union much earlier. The Kama tank school, Lipetsk pilot school and Tomka chemical warfare school all actually predated the Pact by some time, they actually predated Hitler in power, it was
Weimar Germany that was training soldiers in the Soviet Union. Hitler taking power actually put an end to this until the Pact.
As you note, the Allies basically didn't want to know officially. That the Nazis and Soviets were involved in Spain wasn't much of a secret either.
edit: The Allies were trying to play a game in which Germany was restored but not too much militarily unless it was focused East, the whole money laundering scheme they were running on the reparations was part of this. Hitler's being overt with the rearmament was as much of a test as it was in part because it was reaching a point where hiding it wasn't going to be possible without a tacit agreement from the Allies.
Pretty much everything the Allies did after the war with West Germany was because of the experience of trying to do the same thing with Germany between the wars but secretly and "not too much" too quickly.
