I didn't play or even collect much around the Alara storyline, so I didn't pay attention to a lot of the cards in that block until much later, but when I saw Sen Triplets it immediately made me look it up and see what the story is behind the card. Unfortunately, no matter how much I dig I can't seem to find anything. Is this a legend without a story?

Yes.
Alara reborn was particularly rife with loreless legends.

No, but there is M:EM, go write up your own!

There isn't anything even in the fat pack booklet?

Nope. It's divided into two sections: At the End of the Rainbow, which covers the mechanics and touches on the Maelstrom, and The Shards Reborn, which is post-Conflux worlbuilding changes to each shard.

Yes Sin Triple have a big story.