'Check a fact before it's a fact' is a phrase I read in some detective novel when I was a kid. To me it simply means that when faced with a problem, we should thoroughly check the reliability of our information and recognize our assumptions before we make an attempt to solve it.
Checking on the reliability of our information means evaluating the credibility of its source. Does the information come from an acknowledged authority in the subject? What are their credentials? Do they have any bias? Do they cite there work? Is the information current ? If the information comes from a witness to an event, can it be corroborated? Etc. The point is that we should not assume information provided to us is factually true without first doing a little investigating and evaluating.
Recognizing our assumptions means finding those things we may take for granted to be true and evaluating whether or not they are reliable.
The following is a classic (though somewhat dated) example of a problem which demonstrates the tendency to gloss over assumptions:
A father and a his son are involved in a car accident, as a result of which the son is rushed to the hospital for emergency surgery. The surgeon looks at him and says "I can't operate on him, he's my son".
I remember first hearing this riddle when I was a kid and not being able to immediately grasp the obvious answer. Of course the surgeon is the boy's mother. As a culture we are less sexist than we were in my younger years and as such this may no longer be the best example. Lets try another.
A bus driver was heading down a street in Colorado. He went right past a stop sign without stopping, he turned left where there was a “no left turn” sign and he went the wrong way on a one-way street. Then he went on the left side of the road past a cop car. Still – he didn’t break any traffic laws. Why not?
How could the bus driver not be breaking the traffic laws with his apparently reckless actions? Simple; he was walking. Nothing in the riddle says that he was driving but because he is referred to as a bus driver, we tend to first form a mental picture of him or her driving a bus.