I figured it out. There isn't any default disablement of the Button Group - it needs to be coded into the disabled position at the beginning of the code under the _OpeningFcn function. Here is the code:
function MattsTestScript_OpeningFcn(hObject, eventdata, handles, varargin) % Default line produced by GUIDE
handles.output = hObject; % Default line produced by GUIDE
guidata(hObject, handles); % Default line produced by GUIDE
set(findall(handles.MattsButtonGroup, '-property', 'enable'), 'enable', 'off'); % HERE IT IS