Your thoughtful argument has somehow slipped under my radar for almost a year. For this I appologize, and I hope you actually notice this reply.

I think the important thing in a discussion such as this is to first define terms. Most importantly would be to define what is truth. I agree 100% with your definition of a fact:

Facts are specific details that do not change depending upon who observes them.

On the other hand,

"Truth is truth even if no one believes it"

This is inaccurate.

It's not inaccurate at all. Example; "the earth is not the center of the universe" is a true statement. It's true today, it will be true tomorrow, and most importantly, it was true when all humans thought the earth actually was the center of the universe. Truth is unchanging.

Your truth and my truth may both be true as far as we are concerned, but not the same truth.

We live in an age of relative truth. "What's true for you may not be what's true for me" seems to be the comprehensive response in the face of opposing views and opinions. And, it's a truthful statement if we're talking about reality as it pertains to the uniqueness of each person's individual perspective. Unfortunately, when we apply relative truth as a means to understand reality in an objective sense, we are faced with a paradox. You see, the statement "truth is relative" is an absolute statement, and can therefore only be true if it's false!

The facts may show that this man was in the visinity, fits the description of the culprit, fled from police when confronted, etc. All these facts lead to a false conclusion.

Yes, but that was not due to the facts. That was the "truth"/conclusion that the police chose to draw from those facts. That truth is based upon more than just conclusions. It will also be based upon biases, and assumptions.

Let me elaborate: A fact is only a fact if it is true. Yet, in a scenario like the one I describe above, the limited number of facts leed to a false conclusion not because the cops are biased, but because the man is the best suspect based on the available information (I should have said the man was suspected, not accused). So, to suspect and detain this man for questioning is the right thing for the police to do even though their initial suspicions will be proven false.