I think they are being honest.
It is verified for me every time I listen/watch/read conference talks.
It is verified for me when I listen to them in person.
It is verified for me when I do some introspection and see if what they are saying rings true, and if application of those words will make me a better person.
It is verified for me in many, many ways and in all aspects of my life.
It's easy to get so caught up in what we think the "facts" are that we forget to look at the big picture, and we think we are so smart we can figure everything out on our own. We have to be humble enough to know we will need help to figure some, if not many things out.
An interesting thing about today's world, and science, is that we can get so caught up in "proving" a hypothesis wrong over and over again that its pretty easy to forget how to prove something right.
They are telling the truth in most cases and may even be telling to truth in all cases(although this is not likely considering past mistakes), and many things that they say lead many people to better lives. I'm not disputing that this is happening, and I'm absolutely not disputing that your life is benefiting directly from what they teach. The majority of the teachings have value and benefit the world, this is unmistakable.
However, there are things that are hard to explain, things that aren't right. I'm merely exploring the ways in which many people decide to reconcile the differences with what their conscience is saying as opposed to the actions and teachings of their church.
Despite their good words and best intentions, In some ways it's almost impossible for certain people (myself included) to see the First Presidency and Quorum of the Twelve, as prophets, I.E. men who claim to be the mouthpieces of God on this earth. Why? because the amount and frequency of missteps made by these men is very comparable to that of other churches, ones which don't claim exclusivity of priesthood and prophethood, and, of course, some who do.
One may, and many do, expect a church that is actually being led by a prophet, to be a light on a hill, a beacon of enlightenment and strength. A church actually being led by God would somehow differentiate itself among it's peers with an at least better than average track record. Either that or Heavenly Father needs a new PR director. I don't believe he would need one of those.
That's why I believe the way I do. There is no one "true" church, just a handful of great ones, of which the LDS church is a proud member. They are growing, teach great principles and help many people to live better lives, which is absolutely a compliment. And God uses the LDS church to further his goals on this earth, just as he would use other equally worthy establishments. His hands off approach allows room for error in any organization as they are run by humans who make their own decisions. The Prophets of the LDS church are great wise men who are inspired by god and teach important and extremely helpful principles. However, they are not privy to any special information that we, the masses, are not also privy to. Due to the nature of their calling, they are required to make such claims, otherwise they wouldn't be given the authority to, or have the ability to do such good in the world.
Take this with a grain of salt, but my great uncle who was a stake president was taken in for an interview to become a member of the quorum of the seventy. During the course of the interview he had some nagging concerns that he felt needed to be resolved before being moved to his new calling. He asked questions about, you know, the usual stuff: polygamy, priesthood ban, doctrinal inconsistencies, joseph smith issues, and the like. The interviewer responded saying that many if not all members in the higher organization of the church had to make a decision, whether to accept the burden of responsibility the calling requires, ignoring the past issues of the church and aspiring to a position where one could do great good in this world, or giving all of it up through not accepting the position or leaving the church, whatever. They didn't force my great uncle out or anything but he decided on his own that he would leave the church and had his name taken off the records. He joined a christian group in Montana a couple of years ago.
Thanks for reading,
Craig