Are you trying to add buttons to RibbonMenu or RibbonGroup?
In your description you've said you want to add buttons to the menu, but the example you cited is trying to add a button to a ribbon group [I'm assuming group1 is a group not a menu!].
You should be able to add buttons to RibbonMenu, but if it's RibbonGroup you want then you're out of luck.
Here's the code comment for the Items property in RibbonGroup:
// Summary:
// Gets the controls in the group.
//
// Returns:
// The collection of controls in the group.
//
// Exceptions:
// System.InvalidOperationException:
// You try to add, remove, or replace a Microsoft.Office.Tools.Ribbon.RibbonControl
// after the Ribbon is loaded.
IList<RibbonControl> Items { get; }
That's the reason you're getting an error, and that's also why the IsReadOnly property of the collection is set to false.
The Designer needs to be able to modify the items in RibbonGroup when it's creating the ribbon, but once it's loaded you can't make any modifications to it.
Note: If you want to add buttons to RibbonMenu on the fly, set Dynamic to True in your RibbonMenu item properties window (or you could put it in the Designer code), otherwise you'll run into the same exception again.