Unfortunately RadComboBox was not designed to work with a RadGridView inside it (as well as any other control), hence the example you mentioned has certain limitations. You could try to set IsTabStop=false and/or IsFocusable=false on the RadGridView that is inside RadComboBox to prevent it from getting the focus, but I am afraid that we don't have a nice workaround for the problem with the dropdown that stays open.
If you don't need the grid headers, however, you could try with something simpler than a RadGridView - check the following example that demonstrates how to create a custom ItemTemplate for RadComboBox, that could be modified to look very similar to a Grid:
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