Kevin:
According to proper Presbyterian polity, the determination of the first receiving session, insofar as it exercised due discretion in the matter, should be regarded as decisive. Any subsequent sessions, while perhaps taking issue with the original sessional ruling, sure that they would have ruled otherwise, can satisfy themselves that proper process obtained in the ruling of the first receiving session.
A person should not be received with his baptism regarded as valid, only to be told subsequently that it was not and that he must now submit to baptism. This is disorderly and should be considered only in a case where any session would regard the previous baptism as invalid (Mormon baptism, non-Trinitarian baptism, etc.), not in the case where sessions may differ. For example, if a Presbyterian church admits someone on profession of faith, who was baptized in an RCC, a subsequent Presbyterian session that regards RCC baptism as invalid would not properly, on transfer, require the one whom the previous session regarded as validly baptized to submit to rebaptism.
More could be said about why that original session's decision, unless it can be shown to be manifestly wrong (in a way that would withstand scrutiny at appeal), ought to be accepted, but that may be enough for now. Such an action bespeaks congregationalism and not Presbyterianism, which respects decisions of judicatories with which it may disagree as long as those decisions involved a proper act of discretion by the previous judicatory.
Peace,
Alan