The wiki is not authoritative for anything. I am sure my spreadsheet also has errors, but when the wiki says Edinburgh is controlled space that does not mean anything.
The systems that are under direct house government control are listed in the server rules thread here. Go to the bottom and look at the list of house systems that are directly controlled by the house. The systems next to those are within the house ZOI but are not directly controlled by the house, and Edinburgh falls in that category. More specifically Edinburgh is a BW system, that is occupied by two Gallia battleships, so it is more under Gallic control than Bretonian control, and the icon should indiciate this (BW / Galli split with Bretonian influence)