possible. Fun with grammar means exactly what teachers and students should do with grammar: they should have fun with it. For me as a teacher, grammar class is always an opportunity for fun. I cannot imagine dry and dull grammar classes. Fun and humour are essential in grammar classrooms. Interaction and group participation engage students and make information more memorable and relevant. That is how I approach grammar or how I intend teachers to approach. Perhaps it should go without saying, but I am going to say it anyway: I heartily endorse having Fun with grammar!
Inventing a story is a personalised, communicative activity, and often humorous, but unless your students are especially imaginative, it needs some sort of goal or stimulus to keep the story rolling. What I used was simply a list of words written onto cards: each student in turn must take the next word from the card and incorporate it into the story. You could use an object or a picture as a starting-point for the story. Another possible twist is to just make a list of 20 words or so, and then when the class is near the end pick a few groups and ask each person to add a word to the list. I found that students seemed to enjoy doing this. So teachers, don't let the term "grammar" strike fear into the hearts of your learners (or you) ever again. Work up some grammar - teaching activities using different techniques and grammar could become your - and their - favourite lesson type.