For example, if the army keeps launching raids that kill civilians because the government can only track progress through body counts, it is not "facts are the enemy" to stop counting the bodies. (Obviously it would be wiser to stop using the counts as the deciding factor, but if the generals have different values than the government, as immigration courts do, then stopping the count is the only way to stop the bleeding.)
If you were applying for asylum because the conditions in your country were so oppressive to you as a political actor or member of a disfavored ethnic group, you could support your application with relevant data from the CIA world factbook describing general conditions in that country. As a publication of the US government, those factual claims would not be lightly dismissable or disputable the way third party opinions might.