Sigh.. that Sealion pic where Germany controls most of GB is sad... What in the world was the AI doing??? The Royal Navy should have completely shut down all supply routes with no problems... Not only that, but I'm guessing the AI used mostly regular movement instead of strategic movement to try to halt the initial invasions.
It seems you're starting by the presuppose that a german invasion of the UK during WWII was impossible. It´s not that simple, I think.
Germany had the plans, people say that if it weren´t by the USSR invasion they would have tried it.
As a history student, I´ve heard thousand of times that we should not ask ourselves the "what if?" question, but that's why games like HOI3 are for: for us to live a different WWII, but realistic. It's wierd, but it's interesting.
I think it was possible.
For me, sad image is that guy that claims (with a picture) to conquer the East United States by the end of 1938... (with the demo). That simply puts apart the "realistic" factor I said before.