I have downloaded your project and I have run it. It looks to me that it is working well. If you check a checkbox then it becomes checked and any previously checked box becomes unchecked. I imagine that this is what you want to do.
I would make a couple of comments, but they are not very important. Firstly, you probably know that if you use radio buttons then checking one will automatically uncheck all the others (in the same panel/view) without you needing to do anything. But if you want to allow all items to be unchecked (as your example does allow) then you need checkboxes. Secondly, I would use a List rather than a Map; in your example the map functionality is not used.
I think the Erel was just commenting that List.Set is not a common usage, not that there was anything wrong with it. You are not using List.Set in your example anyway, so why worry.