Facts are nice, but fact-checking is not always relevant or helpful, especially when it misses the point of whatever statements are being corrected. At the very least, before jumping at the chance to point out someone’s factual errors, ask:
Is the writer or speaker actually striving for factual accuracy or obviously exaggerating for emotional impact?
Do they appear to be engaging in “loose talk”, carelessly flinging out claims with little regard for accuracy? That is, are they really serious about what they’re saying?
Are they assuming a stance of authority? Are they presenting themselves as a source of expert knowledge? (If so, fact-check away.)
What criteria or values are they using to base their claims? That is, what is their frame of reference?
Why shouldn’t they use those criteria or values?
What type of information do they consider relevant to their claims?
Have you checked out if they have a case for their claims, based on their own criteria or values?
Yeah, that’s a lot of questions. An alternative approach would be to take fact-claims with a certain grain of salt, as possibly or even probably true - but maybe not. And be mindful that too much fact-checking, or relying on fact-checkers, has a chilling effect on independent thought and inquiry (which may in time lead to new facts that replace the old ones).