How Far is Too Far?

According to Mark Twain: "Truth is stranger than fiction, but it is because

Fiction is obliged to stick to possibilities; Truth isn't."

This quote starts to make my brain hurt. I understand the satire, but still, it makes me ponder. If a story is obliged to stick to possibilities, how far is too far when it comes to these story possibilities? Part of me believes that a really talented author can make me believe anything. Yet, anyone who reads narrative fiction has probably had the unfortunate experience of having his or her sense of suspended belief sour into disbelief. This is never pretty. Is this because fiction didn't stick to possibilities, as the great Mark Twain told us?

I think about all the times someone has said to me, usually after some real-life scene when at least one person has behaved really badly or in an absurd or embarrassing way: "Oh, you should write about that." Almost as often, I reply: "Readers would never buy it. Seeing is believing." Truth can be stranger than fiction.

What do you think about Mark Twain's quote? Is anything possible in fiction? If not, how far is too far when dealing with the possibilities? Can you think of an example?

P.S. Does your brain hurt yet?