Did Woodward buy his "religion reporter" credentials at a fire sale? If he thinks Mormons haven't been willing to share their faith, he's not paying attention.
I'm not Morman, so I speak from significant ignorance. But, from my understanding with friends and co-workers who are Mormom, those "many veils" involve practices of the church for members. Become a member, you'll find out what's there. Whether I agree with the LDS church or not, that makes sense to me.
Totally off-topic: One of my favorite movie lines,
Jim Kirk to Jillian in Star Trek IV: The Voyage Home, referring to Spock, Kirk says "He was at Berkeley in the 60s, he did a little too much LDS."
And one rebuttal to your comment about missionaries stealing books from bookstores. Sorry, the Church would never issue orders for missionaries to steal books from bookstores, officially or unofficially.