Yoshi always seems young! Yeah, imagine: "Mario and Luigi found a dinosaur that seemed young in appearance, behavior and speech, but was actually as old as they were."
AND in SMW2, during the opening sequence, the game says, "This is a story about baby Mario and Yoshi" and "Yoshi is taking a leisurely walk" and "Yoshi decides to tell his friends" (some of these aren't exact quotes, my memory isn't photographic) and so on. Over and over again, the game refers to a Yoshi named YOSHI. THE YOSHI.
But about Yoshi Story, you are correct, I don't believe that Yoshi is involved. It's just a bunch of newly hatched yoshies.
-TurtleTek
http://turtletek.botic.com