Pat the pork tenderloin with paper towels to dry. Trim any visible fat and remove the thin, shiny silver skin. Slice it into 1/2-inch thick medallions.
Heat the vegetable oil in a large skillet over medium-high heat. When the oil is hot and shimmering, add the pork slices. Cook until the pork is nicely browned on both sides (about 2 minutes on each side).
Drain pineapple through a colander over a bowl; reserve the juice.
add 2/3 cups of water, vinegar, soy sauce, brown sugar, and salt to the reserved juice. Pour over the pork tenderloin. Bring to a boil. Reduce heat to low, cover the pan, and simmer for 5 minutes. Remove the pork pieces and keep warm.
In a cup or bowl, combine the cornstarch and 3 tablespoons of water; stir until smooth. Add the cornstarch and water mixture to the skillet. Cook over low heat, stirring constantly, until the sauce is thickened and bubbly.
Add the pineapple tidbits, onion, and green pepper to the skillet. Cover and simmer for about 10 minutes longer or until vegetables are tender. Add the pork back to the skillet and heat through.