It's a long-standing gotcha which amounts to MatrixForm being (arguably) badly designed. If one uses e.g. InputForm or FullForm then the formatting is applied and the wrapper disappears. The MatrixForm wrapper alas does not disappear. So instead of a rectangular list of lists, the structure is MatrixForm[list-of-lists].
Maybe this rewriting of your example will help to clarify. (For display purposes I converted the Out[1] cell to InputForm so it would avoid showing a mess of linear syntax.)
In[1]:= e1 = MatrixForm[{{0.2, 0.1, 0.1}, {0.1, 0.2, 0.2}, {0.1, 0.1, 0.3}}]
(* Out[1]//MatrixForm= MatrixForm[{{0.2, 0.1, 0.1}, {0.1, 0.2, 0.2}, {0.1, 0.1, 0.3}}] *)
In[2]:= MatrixQ[e1]
(* Out[2]= False *)
In[4]:= {Head[e1], MatrixQ[e1[[1]]]}
(* Out[4]= {MatrixForm, True} *)