The reasoning behind the increased air space is exactly as you say, it increases the agitation. However; when the tank is inverted, the air chases the developer out from between the layers of film more completely, so that when the tank is brought back right way up, then less-exhausted developer can flood back in. The result should be, not that the edges receive less development, but that the centre of the film receives more.(posted 8670 days ago)
Agitation doesn't actually increase the developer's activity, it simply replaces exhausted developer with fresher stuff, allowing the proper rate of development to take place.