The phrase 'closing the doors properly' is impersonal - it does not indicate who or what is the grammatical subject that performs the action of closing. The original sentence is clear about this - the doors are the passive grammatical subjects: 'the doors are properly closed'. Answer choice E preserves the passive construction and hence the meaning of the original sentence.
Because it is phrased impersonally, answer choice D could be misconstrued to mean that the design of the latches assure 'someone's' closing the door, but the latches are part of the door mechanism - they do not assure that the person closing the door will perform a correct action, close it properly but rather that the physical object - the door - will be closed properly (and stay closed).

Thanks Ilana!