I'm not sure that spying was "hyped" to cover up Enigma per say, but very few people actually knew where Ultra information came from. Even people who worked at Bletchley Park didn't actually know the entire process / system.

I have read that some people were left to assume that 'Ultra' was a spy, all they were told was it was an intelligence source.

What the Allies definitely did do was to not exploit Ultra information to the fullest extent, for fear of giving the game away. Even if they did use the information they'd provide a reasonable explanation, for example Ultra revealed that the Tirpitz and been moved to a certain Fjord. Rather than use this directly they sortied a photo reconnaissance aircraft to fly over the area, making its presence quite clear and then mounted attacks.

The Allies also planted misleading information. The best example is surely Operation Fortitude that sought to mislead the Axis on the location of the D-Day landings. The US 1st Army group was created purely to mislead the Germans, men trampled around fields to make it look like an army was there, they also put inflatable aircraft and tanks in fields to make it look like there was a build up of men and weapons. In reality, none of it existed. At the same time they also fed false information through double agents like Juan Pujol Garcia (codename Garbo). Ultra was important here as they used it to double check the right message was getting to the German High Command and that they issued orders that the Allies wanted to the German forces.

After the war and the start of the cold war I don't think anyone wanted to give away what they did or didn't know with regards to encryption and codebreaking.