Hi BrowserUK,
your analysis is perfectly true and you are describing the algorithm I just implemented. The magenta circle is essentially picture 1 of my post.
But lets consider again this picture: http://www.myimg.de/?img=tile2a1863.png - how would you achieve that the distance of the uppermost green tile has the same distance to the circle as the lower left green tile? I don't think that this can be achieved by placing the center of the circle to any of the four points you mention ...
The tricky think is to move the center of the circle such that the beholder "thinks", the tiles are centered. Please look at my last pic (http://www.myimg.de/?img=tile417dd5.png) where the optical glitch of a nonsymmetric tile array becomes obvious ...