How intriguing. I'm arguing with someone with whom I somewhat agree.
Anyone familiar with dictionaries will know many words which are very important to us have several to many related definitions.
My old Webster New World Dictionary of the American Language has five. Among them are: something said to have occurred or supposed to be true and an actual or alleged incident or condition.
My even older Webster's Third New International Dictionary has six rather rigorous definitions, among them are: an assertion, statement, or information containing or purporting to contain something having objective reality and any of the circumstances of a case at law as it exists or is alleged to exist in reality; something proved by the evidence to be or alleged to be of actual occurrence.
So, to repeat the statement, the problem is both sides dispute the other side's facts.
And, I do agree, there are many half-truths, lies and agendas spewing forth. Because the Schindler's forensic pathologist's request to observe the autopsy was refused by the medical examiner, you can bet those half-truths, lies and agendas will have a long, long shelf life.
American Heritage fourth ed.
Semantics--I happen to think a fact is true and other usages can lead to ambiguity, as here. In any event we agree that this case is full of lies and half truths.