Have you determined if the problem(s) disappear if you remove/disable the adapters?
To do so, you would temporarily get rid of the .browser file(s) you have in your App_Browsers folder. It is in those .browser files that the adapters get enabled. Temporarily getting rid of those files means you run you pages with the built-in ASP.NET rendering.
So, you would want to test that the problem does (or doesn't) occur if you disable the adapters.
As the author of the adapters I can tell you that I didn't put anything special into them to deal with security trimming. I felt that that should be left up to the data provider that feeds the treeview or menu. Do you agree?