http://www.apple.com/uk/batteries/iphone.html
"Enable Wi-Fi: Having Wi-Fi enabled helps consume less power when doing activities that access data. Go to Settings > Wi-Fi and log in to a Wi-Fi network."
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I don't think this conflicts with the idea that, when idle, shutting off wifi will improve battery life. The above advice just says that wifi consumes less than 3G when accessing data. What I get from this is, e.g. if you download lots of data over 5 minutes, it's more efficient to do this over wifi. But if you are downloading no data over 5 mins, shutting down wifi will use less battery during that 5 mins than if you left it on.
Push notifications you might receive during idle are probably so small that there are more gains in turning off wifi than leaving it on (assuming a long enough idle period and not many notifications).
Who knows what sort of intelligent stuff is built into the OS management of radios- it's quite hard to tell when the screen is off! But here are some ideas just to stretch your imagination.
Perhaps if you receive a lot of push notifications when idle, Apple learns from this and keeps wifi active during times when it thinks lots of notifications might come in.
Perhaps when an email header is pushed to the phone over 3G, it connects to wifi to download the body.
Perhaps during idle when apps are refreshing in the background (new iOS 7 feature), it connects to wifi to download/upload any data.
But if your phone is not actively doing anything, and if the only data activity might be the odd notification (which are only a few kb), it probably pays off to turn off wifi. They are also so small that they probably won't even upset people with little data on their contract.
