Learn English – Meaning of seeming contradiction

NOAD gives this listing:

fact |fakt| noun a thing that is indisputably the case : she lacks political experience—a fact that becomes clear when she appears in public | a body of fact.

So it would seem that something that is "indisputably the case" could not be "incorrect"; and I am sure that, strictly speaking, this is a fact.

Nevertheless, very often people state as fact what is merely opinion. In fact, whenever you hear someone start a sentence with "the fact is" or "in fact" you are well advised to weigh carefully whatever claim is being made.

We also hear people speaking of "true facts" (which surely should be a redundancy) and "alleged facts". In the sense that anything can be true, a fact must be true, but what is true is almost always negotiable. Something that is not proven should not be called factual, though people do it all the time.

Where does that leave us? I myself would avoid using qualifiers with the word "fact" but I would tolerate it in others; but then, I always weigh the claims made by others (especially news writers), and I advise others to do the same.

The meaning here is quite specific. A team controls its own destiny if it reaches the playoffs by winning all its remaining games regardless of the outcome of other games.

So, for example: Suppose there is one game remaining, Teams A and B are tied in the standings with one to qualify for the playoffs, and Team A has a tie-breaking advantage over Team B for some reason. In the last regular game, A plays C and B plays D. A controls its destiny: it qualifies with a win over C. B does not. It needs not only to win, but moreover for A to lose. (Modify as necessary for games where draws occur.)