Truth is stranger than fiction, but it is because Fiction is obliged to stick to possibilities; Truth isn't.
The first half of that supporting statement is rather obvious: “fiction is obligated to stick to possibilities.” Once you build a fictional world and characters, you have to be consistent. The second half statement, “truth isn’t,” is profound. Real life and real people don’t have to be consistent because very often real life is not, and real people are most definitely not.
The quote is also interesting because a reader will not believe an author when he is inconsistent because he feels it violates real life. But real life violates real life all the time, and we feel comfortable with that.