Giving up precision is different to giving up the narrative. The narrative can be helped by engagement and if that comes at the cost of precision, then that was the cost of getting the message further than it may have otherwise reached.

In this case, what is meant by "give up some precision" is to try removing some sharp edges that get in the way of telling the story. It's a long way from lying (when done with due consideration).

They're examples. Choose what works for your data and you your story to get the best result.