I've served as an RCIA (Rite of Christian Initiation of Adults) instructor. One of the questions they ask right off the bat is whether the person has previously joined a Christian Church and accepted Christ. If not, the RCIA process takes a lot longer. For example, we had a Muslim interested in becoming Catholic, but he was nowhere near as familiar with the scripture and basic Christian doctrines like original sin as the person who was raised Lutheran had been. The Muslim convert attended different classes than my brother-in-law and his niece, because the latter two had already been baptized years ago. The non-Christians can be initiated into the Catholic Church at the same Mass as the people who are already Christians, but the process leading up to that day takes a lot longer for the non-Christians, because we have to make sure they fully understand and accept Christ before they are received into the church. Those who have been already baptized are asked to provide a baptismal certificate so the parish sponsoring them can confirm its a valid baptism.
It's possible Jindal didn't have proof of his baptism with him or was just confused and didn't realize he was already Christian by being baptized in a Baptist Church, but I doubt it. If he was a Hindu considering joining a Catholic Church, the process would have been quite different.
In any case, its a matter of splitting hairs. Whether Jindal was baptized in the SBC or the Catholic Church, he has a valid a Christian baptism.
It's possible Jindal didn't have proof of his baptism with him or was just confused and didn't realize he was already. Sure, he was already saved by a minister and makes that clear, but he may have been re-baptized for the reasons you mentioned, or even because he seems so passionate about religion, that he may have felt better getting a Catholic baptism as a personal event in his becoming a full Catholic, and just handled things in a way, that he got one.