The unfortunate thing is that they don't really know if they are right. Nobody really knows until it's all over. When people tell me that they know that it is true, what they are really saying is that they hope and very strongly believe that it is true. But belief and hope do not equal knowledge. Most claim to "know" because they have had an emotional/spiritual experience that has confirmed the truth of these things to them. I think what is interesting is that these individuals feel that their spiritual experiences are unique to their own religion (contrasts).
Surely suicide bombers know that what they do is right and good. Surely the 7th-Day Adventists know that their interpretation of Christ's teachings is the correct one.
Yet members of the LDS church discount these individuals' knowledge. "Oh, they can't really know. They just think they do. But I know. I'm different."
It's interesting to study the history of the Church and see just how many of those in Joseph Smith's elite inner circle left the Church or denied Smith's prophetic calling at some point. Didn't they also "know?" Didn't they also have experiences that they felt they couldn't deny? Why did so many choose to follow apparently false prophets after Smith's death (e.g., James Strang)? Didn't they use the same spiritual confirmations with Strang as they did with Smith? Was one confirmation from God and the other from the Devil, but they were too similar to tell apart? The crux of the problem here is that these individuals used the same source (i.e., the Holy Ghost) to reach incompatible conclusions (i.e., both Smith and Strang were inspired prophets).
The Church asks every investigator to step back for a moment and consider the possibility that the core beliefs they hold are not 100% accurate. They ask each person to be like a child; submissive, meek, humble, willing to submit... (Mosiah 3:19). Yet it seems that so many are unwilling to do the same when presented with questions regarding their own faith. So many are unwilling to take a humble stance about their "knowledge" of the Church, but choose and are encouraged to follow only the initial feelings they have when hearing about the positive side of Joseph Smith and the Church, and then to insist that that means they know that all evidence to the contrary is a lie, usually without becoming familiar with it.
Albert Einstein said something to the effect of "How we see things determines what we see." And so perhaps what we know is more determined by the way we choose to look, or choose not to look, at the world. Perhaps what we know is not knowledge at all, but only our best understanding of the information we have so far. Maybe if we are willing to change how we look at things, we can see them for what they really are.