There should be a way to exclude the partially checked items from the CheckedItems collection. 
A a property can be added to specify whether they will be included.

Edit: Please avoid using this collection because it ihas never been implemented completely in the RadTreeView. In DataBinding scenarios, you can use CheckBox in the ItemTemplate of the RadTreeView. Approach can be found here =>
http://docs.telerik.com/devtools/wpf/controls/radtreeview/how-to/howto-tri-state-mvvm.html 
CheckedItems colelction can be implemented in the ViewModels, instead of using the built-in property.

The XAML team has recently reviewed this issue and will not be addressing it as at this time the team is focusing on the bugs impacting the highest number of developers. If you have encountered this issue and it is blocking for your work please contact us through the support ticketing system with details on your setup and a reference to this item.