Since there is a means to go by in judging through the real owner of a child being born, we can always result for DNA test in doing that, but its such a pity that even in some areas where truth is far from being established in their endeavors, they will try to manipulate the DNA result and present a fake one through the influence of someone involved who is influential financially, truth is sometimes far away from any process we go through if we are not dealing with the right ones.
DNA can be conducted from multiple labs, this way it becomes impossible for any of the partners to temper with the result of the DNA, what you said can only happen when the test is carried out I just one hospital, most case will result to multiple results to avoid manipulation.
Time have advanced and people are smarter a d well informed than before so for sure, any attempt to crest deceit will always be quickly noticed and such attempts are swept under the carpet.