The complete sentence runs as follows:
The judges unanimously disagreed that he was fit to compete.
What does it mean?
The complete sentence runs as follows:
The judges unanimously disagreed that he was fit to compete.
What does it mean?
Someone was asserting that he was fit to compete. The judges all disagreed with that statement. In other words, the judges all disagreed with the statement that he was fit to compete; in other words, the judges all disagreed that he was fit to compete; in other words, the judges unanimously disagreed that he was fit to compete.
Not exactly a specimen of good writing, I have to say…
[Edit: Dan points out, and I agree, that this could also be 'a deliberate play of on words from the standard unanimously agreed used for effect'.]
Here's what it means:
All of the judges decided that he was unfit to compete.
The key here is recognising that "disagreed" isn't standing on its own. It's actually paired with the following phrase - "disagreed that (assertion)", and loses its meaning if separated.
You can say that "the panel unanimously agreed" without saying what they agreed on; you can't say that some people unanimously disagreed without knowing the idea (at least implied) with which they disagreed.
We could expand the original sentence to make it clearer: "The judges were unanimous: each one disagreed that he was fit to compete."
A version where the claim is implicit: "He said he was fit to compete. The judges unanimously disagreed."