"distressing fact" is correct and usable in written English.
You can use it to refer to a problem, issue, circumstance, or situation that is difficult or unpleasant to accept. For example, "The distressing fact is that poverty levels in this city are increasing."
Washington's cooperation with the Northern Alliance also reflects a distressing fact.
It is a distressing fact of life that mistreatment of Muslims does not draw nearly the protest that it should.
A distressing fact: I found out by not being able to use my iPod to DJ in Glasgow that Jasper's iPod has no David Bowie in it whatsoever.
But it points once again to the distressing fact that New York's disclosure law gives the public far less access to information about police officers than workers in virtually any other public agency.
That distressing fact is mainly courtesy of our current energy source of choice — the burning of fossil fuels, a process by which Earth's carbon stores are essentially excavated from their natural position in the global carbon cycle and released into the atmosphere as greenhouse gas.
Another distressing fact: Roughly two in five South Africans have no job.
One of the most distressing facts about Wednesday's release of the Overcoming Indigenous Disadvantage report is that tragic news like this is becoming more common.
The distressing facts about Detroit are by now almost a cliché: 40 percent of streetlights were not working this spring, tens of thousands of buildings are abandoned, schools have closed and the population declined 25 percent in the last decade alone.
Carl Safina has partly solved that problem — by assembling a dossier of intriguing information about sea turtle biology and distressing facts about what humans have done to push these creatures toward extinction.
Two distressing facts about the nation's youth bode ill for their future well-being: American children today are fatter than ever and less fit than they were in the 1960's, when John F. Kennedy established the President's Council on Physical Fitness.
"Notwithstanding the distressing facts of his situation, the defendant submits that the claim for declarations is untenable.
