I read Copi's 'Introduction to Logic 8th ed." and he says that even if we are using the truth table of the implication in the restricted sense ( as compared to the usage of the implication in the regular language), the validity of the arguments is preserved if we use the truth table of the material implication (that's what he calls it). And
he demonstrates it with some examples. So that is I think satisfactory answer to all the nagging doubts. After all , what matters is , whether the validity of
the arguments is intact after translating ordinary sentences into the language of the symbolic logic.