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.
The Catholic initiations I've attended for adults are public events, and usually performed as Easter vigil services with the whole community present.
That being said, if I had to guess, the most likely scenario is that Jindal did not receive a baptism upon joining a Catholic Church, but rather a Confirmation and Holy Communion. Agree its an interesting question, and one of the media likely won't cover.
A more important question, also avoided by the media, is whether Obama was EVER baptized. It appears his daughters were baptized by Obama's hate whitey pastor, but I've ever heard any account of Obama being baptized himself, either before or after joining Trinity UCC. Merely attending his wife's hate whitey church doesn't make him a Christian, and the vast majority of Catholic and Protestant churches agree on that point. People argued about Obama's birth certificate for years, while no one investigated whether self-proclaimed "Christian" Obama had actually become a Christian. Since he gets so offended by suggetions that he's not Chrisitan, the burden should be on him to demostrate that he became a Christian on so-and-so date.