Whilst the sky under the bird is a good rule of thumb for pheasants, it certainly wouldn't do on a grouse moor and I've shot on partridge shoots where it does not apply.
However, safety first and if in doubt, don't shoot. Usually the shoot captain will explain where and when you can take the grouse or partridge below the skyline.
Interesting that you have had positive experiences bringing a gun into the country and I was glad to read that. I've flown a few times with a gun and never had a problem, lots of curiosity dressed up as officialdom, though!
Tim
