Wow, obviously you didn't look at the site very closely. You have to register yourself in order to be listed. Jacob registered himself. Derek did not. How do I know this besides the obvious website? I tried to look up my husband, who I know served a successful 2-year mission-- I've met his mission president, gone to missionary reunions, even been to the country he served, and he isn't listed. I also tried several of his friends. Not listed. I also tried my father-- not listed. Maybe you're the one who needs to check your facts before you start making accusations about truth.
Look, the only information I can offer is what I know. I know Derek went on a mission because I remember seeing him the day before he went in the MTC. I remember hearing updates on his progress from my father and ward members. I've seen pictures of him there. I saw his name and mission address listed on the back of the ward programs at church where they list all the missionary locations so you can write to them. And I remember when he got home. So, you may not be able to find evidence, but I KNOW he went on a mission. I will do my best to track down some kind of listing or see if I have one of the church programs in a scrapbook or something.
As far as him going off the deepend, I feel it's very sad. I too think it's disturbing. And Shiloh too, who was such a cute and good girl growing up. Yes, they have their problems, but they were active at one time-- very active in the church. Not eveyone that has ever been a member of the church is still a member. My husband has an uncle who went on a mission, got married in the temple, graduated from BYU, and now he also lives a quite alternative life.